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Volumn , Issue , 2011, Pages 1-306

The Cauchy–Schwarz master class: An introduction to the art of mathematical inequalities

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EID: 84923210330     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511817106     Document Type: Book
Times cited : (384)

References (149)
  • 1
    • 84923117757 scopus 로고
    • Ungleichungen und ihre verwendung zur elementaren lösung von maximum- und minimumaufgaben
    • Aczél, J. (1961/1962). Ungleichungen und ihre Verwendung zur elementaren Lösung von Maximum- und Minimumaufgaben, L’Enseignement Math. 2, 214–219.
    • (1961) L’Enseignement Math , vol.2 , pp. 214-219
    • Aczél, J.1
  • 4
    • 0010162730 scopus 로고
    • Grüss’ inequality for positive linear functional
    • Andrica, D. and Badea, C. (1988). Grüss’ inequality for positive linear functional, Period. Math. Hungar., 19, 155–167.
    • (1988) Period. Math. Hungar , vol.19 , pp. 155-167
    • Andrica, D.1    Badea, C.2
  • 5
    • 0002358720 scopus 로고
    • Über die zerlegung definiter funktionen in quadrate
    • Artin, E. (1927). Über die Zerlegung definiter Funktionen in Quadrate, Abh. Math. Sem. Univ. Hamburg, 5, 100-115.
    • (1927) Abh. Math. Sem. Univ. Hamburg , vol.5 , pp. 100-115
    • Artin, E.1
  • 6
    • 0003406635 scopus 로고    scopus 로고
    • 2nd Edition, Springer-Verlag, Berlin
    • Bak, J. and Newman, D.J. (1997). Complex Analysis, 2nd Edition, Springer-Verlag, Berlin.
    • (1997) Complex Analysis
    • Bak, J.1    Newman, D.J.2
  • 7
    • 0141693771 scopus 로고    scopus 로고
    • An elementary introduction to modern convex geometry
    • (S. Levy, ed.), MSRI Publications, Cambridge University Press, Cambridge, UK
    • Ball, K. (1997). An elementary introduction to modern convex geometry, in Flavors of Geometry (S. Levy, ed.), MSRI Publications 31 1–58, Cambridge University Press, Cambridge, UK.
    • (1997) Flavors of Geometry , vol.31 , pp. 1-58
    • Ball, K.1
  • 8
    • 0004346603 scopus 로고    scopus 로고
    • (translated by Abe Shenitzer, originally published by Nauka, Moscow, 1972), Mathematical Association of America, Washington D.C
    • Bashmakova, I.G. (1997). Diophantus and Diophantine Equations (translated by Abe Shenitzer, originally published by Nauka, Moscow, 1972), Mathematical Association of America, Washington D.C.
    • (1997) Diophantus and Diophantine Equations
    • Bashmakova, I.G.1
  • 9
    • 0004168362 scopus 로고
    • (2nd revised printing), Springer-Verlag, Berlin
    • Beckenbach, E.F. and Bellman, R. (1965). Inequalities (2nd revised printing), Springer-Verlag, Berlin.
    • (1965) Inequalities
    • Beckenbach, E.F.1    Bellman, R.2
  • 11
    • 0034344488 scopus 로고    scopus 로고
    • Using integral transforms to estimate higher order derivatives
    • Bradley, D. (2000). Using integral transforms to estimate higher order derivatives, Amer. Math. Monthly, 107, 923–931.
    • (2000) Amer. Math. Monthly , vol.107 , pp. 923-931
    • Bradley, D.1
  • 13
    • 0040179173 scopus 로고
    • Sur quelques inégalités concernant les intégrales ordinaires et les intégrales aux différences finies
    • (ser. 7)
    • Bouniakowsky, V. (1859). Sur quelques inégalités concernant les intégrales ordinaires et les intégrales aux différences finies. Mémoires de l’Acad. de St.-Pétersbourg (ser. 7) 1, No. 9.
    • (1859) Mémoires De l’Acad. De St.-Pétersbourg , vol.1 , Issue.9
    • Bouniakowsky, V.1
  • 16
    • 84880928473 scopus 로고
    • The william lowell putnam mathematical competition
    • Bush, L.E. (1957). The William Lowell Putnam Mathematical Competition, Amer. Math. Monthly, 64, 649–654.
    • (1957) Amer. Math. Monthly , vol.64 , pp. 649-654
    • Bush, L.E.1
  • 18
    • 0041362825 scopus 로고
    • Generalizzazione della disegualianza di cauchy–schwarz
    • Buzano, M.L. (1971/1973). Generalizzazione della disegualianza di Cauchy–Schwarz, Rend. Sem. Mat. Univ. e Politech. Trimo, 31, 405–409.
    • (1971) Rend. Sem. Mat. Univ. E Politech. Trimo , vol.31 , pp. 405-409
    • Buzano, M.L.1
  • 19
    • 0004209478 scopus 로고
    • (translation ofThéorie élémentaire des fonctions analytiques d’une ou plusieurs vairable complexes, Hermann, Paris, 1961) reprinted by Dover Publications, Mineola, New York
    • Cartan, H. (1995). Elementary Theory of Analytic Functions of One or Several Complex Variables (translation of Théorie élémentaire des fonctions analytiques d’une ou plusieurs vairable complexes, Hermann, Paris, 1961) reprinted by Dover Publications, Mineola, New York.
    • (1995) Elementary Theory of Analytic Functions of One or Several Complex Variables
    • Cartan, H.1
  • 20
  • 21
    • 0005435139 scopus 로고
    • A proof of an inequality of carleman
    • Carleson, L. (1954). A proof of an inequality of Carleman, Proc. Amer. Math. Soc., 5, 932–933.
    • (1954) Proc. Amer. Math. Soc , vol.5 , pp. 932-933
    • Carleson, L.1
  • 24
    • 84923177715 scopus 로고
    • An inductive proof of the a.M.–g.m. inequality
    • Chong, K.-M. (1969). An inductive proof of the A.M.–G.M. inequality, Amer. Math. Monthly, 83, 369.
    • (1969) Amer. Math. Monthly , vol.83 , pp. 369
    • Chong, K.-M.1
  • 25
    • 0023995533 scopus 로고
    • Self-organizing sequential search and hilbert’s inequalities
    • Chung, F.R.K., Hajela, D., and Seymour, P.D. (1988). Self-organizing sequential search and Hilbert’s inequalities, J. Computing and Systems Science, 36, 148–157.
    • (1988) J. Computing and Systems Science , vol.36 , pp. 148-157
    • Chung, F.1    Hajela, D.2    Seymour, P.D.3
  • 26
    • 51949114791 scopus 로고
    • Majorization and the birthday problem
    • Clevenson, M.L., and Watkins, W. (1991). Majorization and the Birthday Problem, Math. Magazine, 64, 183–188.
    • (1991) Math. Magazine , vol.64 , pp. 183-188
    • Clevenson, M.L.1    Watkins, W.2
  • 28
    • 84966242118 scopus 로고
    • On hilbert’s inequality in n dimensions
    • de Bruijn, N.G. and Wilf, H.S. (1962). On Hilbert’s inequality in n dimensions, Bull. Amer. Math. Soc., 69, 70–73.
    • (1962) Bull. Amer. Math. Soc , vol.69 , pp. 70-73
    • De Bruijn, N.G.1    Wilf, H.S.2
  • 29
    • 0013027251 scopus 로고
    • 2nd Edition, Harcourt, Brace, Javonovich, New York
    • Davis, P.J. (1989). The Thread: A Mathematical Yarn, 2nd Edition, Harcourt, Brace, Javonovich, New York.
    • (1989) The Thread: A Mathematical Yarn
    • Davis, P.J.1
  • 30
    • 84966249826 scopus 로고
    • Stronger forms of a class of inequalities of g. Pólya–g. szegő, and l.v. kantorovich
    • Diaz, J.B. and Metcalf, R.T. (1963). Stronger forms of a class of inequalities of G. Pólya–G. Szegő, and L.V. Kantorovich, Bulletin of the Amer. Math. Soc., 69, 415–418.
    • (1963) Bulletin of the Amer. Math. Soc , vol.69 , pp. 415-418
    • Diaz, J.B.1    Metcalf, R.T.2
  • 31
    • 4644373794 scopus 로고
    • A complementary triangle inequality in hilbert and banach spaces
    • Diaz, J.B. and Metcalf, R.T. (1966). A complementary triangle inequality in Hilbert and Banach spaces, Proc. Amer. Math. Soc., 17, 88–97
    • (1966) Proc. Amer. Math. Soc , vol.17 , pp. 88-97
    • Diaz, J.B.1    Metcalf, R.T.2
  • 32
    • 0346388273 scopus 로고    scopus 로고
    • On the cauchy–buniakowsky–schwarz inequality for sequences in inner product spaces
    • Dragomir, S.S. (2000). On the Cauchy–Buniakowsky–Schwarz inequality for sequences in inner product spaces, Math. Inequalities Appl., 3, 385–398.
    • (2000) Math. Inequalities Appl , vol.3 , pp. 385-398
    • Dragomir, S.S.1
  • 35
    • 17844401814 scopus 로고
    • Cauchy–bunyakowski–schwarz revisited
    • Dubeau, F. (1990). Cauchy–Bunyakowski–Schwarz Revisited, Amer. Math. Monthly, 97, 419–421.
    • (1990) Amer. Math. Monthly , vol.97 , pp. 419-421
    • Dubeau, F.1
  • 37
    • 84963044709 scopus 로고
    • A simple extension of some recently proved facts as to convergency
    • Elliot, E.B. (1926). A simple extension of some recently proved facts as to convergency, J. London Math. Soc., 1, 93–96.
    • (1926) J. London Math. Soc , vol.1 , pp. 93-96
    • Elliot, E.B.1
  • 39
    • 0342482605 scopus 로고
    • Problems and results on the theory of interpolation ii
    • Erdős, P. (1961). Problems and results on the theory of interpolation II, Acta Math. Acad. Sci. Hungar., 12, 235–244.
    • (1961) Acta Math. Acad. Sci. Hungar , vol.12 , pp. 235-244
    • Erdős, P.1
  • 40
    • 84923193394 scopus 로고
    • Über eine ungleichung von s.S. wagner
    • Flor, P. (1965). Über eine Ungleichung von S.S. Wagner, Elem. Math., 20, 165.
    • (1965) Elem. Math , vol.20 , pp. 165
    • Flor, P.1
  • 41
    • 84968495078 scopus 로고
    • Buzano’s inequality and bounds for roots of algebraic equations
    • Fujii, M. and Kubo, F. (1993). Buzano’s inequality and bounds for roots of algebraic equations, Proc. Amer. Math. Soc., 117, 359–361.
    • (1993) Proc. Amer. Math. Soc , vol.117 , pp. 359-361
    • Fujii, M.1    Kubo, F.2
  • 43
    • 0040072699 scopus 로고    scopus 로고
    • Lecture Notes in Mathematics No. 1679, Springer-Verlag, Berlin
    • Grosse-Erdmann, K.-G. (1998). The Blocking Technique, Weighted MeanOperators, and Hardy’s Inequality, Lecture Notes in Mathematics No. 1679, Springer-Verlag, Berlin.
    • (1998) The Blocking Technique, Weighted Mean
    • Grosse-Erdmann, K.-G.1
  • 44
  • 45
    • 84923177713 scopus 로고    scopus 로고
    • Technical Report, Institute of Problems of Information Technology, Moscow, Russia
    • Hammer, D. and Shen, A. (2002). A Strange Application of Kolmogorov Complexity, Technical Report, Institute of Problems of Information Technology, Moscow, Russia.
    • (2002) A Strange Application of Kolmogorov Complexity
    • Hammer, D.1    Shen, A.2
  • 46
    • 0000244508 scopus 로고
    • Note on a theorem of hilbert
    • Hardy, G.H. (1920). Note on a theorem of Hilbert, Math. Zeitschr., 6, 314–317.
    • (1920) Math. Zeitschr , vol.6 , pp. 314-317
    • Hardy, G.H.1
  • 47
    • 0001665563 scopus 로고
    • Notes on some points in the integral calculus (lx)
    • Hardy, G.H. (1925). Notes on some points in the integral calculus (LX), Messenger of Math., 54, 150–156.
    • (1925) Messenger of Math , vol.54 , pp. 150-156
    • Hardy, G.H.1
  • 48
    • 0013209480 scopus 로고
    • A note on two inequalities
    • Hardy, G.H. (1936). A Note on Two Inequalities, J. London Math. Soc., 11, 167–170.
    • (1936) J. London Math. Soc , vol.11 , pp. 167-170
    • Hardy, G.H.1
  • 50
    • 0000600466 scopus 로고
    • Some simple inequalities satisfied by convex functions
    • Hardy, G.H., Littlewood, J.E., and Pólya, G. (1928/1929). Some simple inequalities satisfied by convex functions, Messenger of Math., 58, 145–152.
    • (1928) Messenger of Math , vol.58 , pp. 145-152
    • Hardy, G.H.1    Littlewood, J.E.2    Pólya, G.3
  • 51
  • 53
    • 0003603456 scopus 로고
    • Two remarks on the kantorovich inequality
    • Henrici, P. (1961). Two remarks on the Kantorovich inequality, Amer. Math. Monthly, 68, 904–906.
    • (1961) Amer. Math. Monthly , vol.68 , pp. 904-906
    • Henrici, P.1
  • 55
    • 0000432495 scopus 로고
    • Über die darstellung definiter formen als summe von formenquadraten
    • (Also inGesammelte Abhandlungen, Volume 2, 154–161, Springer-Verlag, Berlin, 1933; reprinted by Chelsea Publishing, New York, 1981.)
    • Hilbert, D. (1888). Über die Darstellung definiter Formen als Summe von Formenquadraten, Math. Ann., 32, 342–350. (Also in Gesammelte Abhandlungen, Volume 2, 154–161, Springer-Verlag, Berlin, 1933; reprinted by Chelsea Publishing, New York, 1981.).
    • (1888) Math. Ann , vol.32 , pp. 342-350
    • Hilbert, D.1
  • 56
    • 0002849569 scopus 로고
    • Mathematische probleme
    • 213237 (Also inGesammelte Abhandlungen,3, 290–329, Springer-Verlag, Berlin, 1935; reprinted by Chelsea, New York, 1981; translated by M.W. Newson inBull. Amer. Math. Soc., 1902,8, 427–479.)
    • Hilbert, D. (1901). Mathematische Probleme, Arch. Math. Phys., 3, 44-63, 213–237. (Also in Gesammelte Abhandlungen, 3, 290–329, Springer-Verlag, Berlin, 1935; reprinted by Chelsea, New York, 1981; translated by M.W. Newson in Bull. Amer. Math. Soc., 1902, 8, 427–479.).
    • (1901) Arch. Math. Phys , pp. 44-63
    • Hilbert, D.1
  • 58
    • 34250609333 scopus 로고
    • Sur les fonctions convexes et les inégalités entre les valeurs moyennes
    • Jensen, J.L.W.V. (1906). Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta Math., 30, 175–193.
    • (1906) Acta Math , vol.30 , pp. 175-193
    • Jensen, J.1
  • 59
    • 0003375593 scopus 로고
    • Birthday problem with unlike probabilities
    • Joag-Dev, K. and Proschan, F. (1992). Birthday problem with unlike probabilities, Amer. Math. Monthly, 99, 10–12.
    • (1992) Amer. Math. Monthly , vol.99 , pp. 10-12
    • Joag-Dev, K.1    Proschan, F.2
  • 61
    • 0004057127 scopus 로고
    • second Edition, Chelsea Publishing, New York (1st Edition, Warsaw, 1935)
    • Kaczmarz, S. and Steinhaus, H. (1951). Theorie der Orthogonalreihen, second Edition, Chelsea Publishing, New York (1st Edition, Warsaw, 1935).
    • (1951) Theorie Der Orthogonalreihen
    • Kaczmarz, S.1    Steinhaus, H.2
  • 62
    • 33845643825 scopus 로고    scopus 로고
    • manuscript based on notes for the Math Olympiad Program, MIT, Cambridge MA
    • Kedlaya, K. (1999). A < B (A is less than B), manuscript based on notes for the Math Olympiad Program, MIT, Cambridge MA.
    • (1999) A < B (A is less than B)
    • Kedlaya, K.1
  • 63
    • 0000501688 scopus 로고    scopus 로고
    • Szemeredi’s regularity lemma and its applications in graph theory
    • (D. Miklós, V.T. Sos, and T. Szőnyi, eds.), János Bolyai. Mathematical Society, Budapest
    • Komlós, J. and Simomovits, M. (1996). Szemeredi’s regularity lemma and its applications in graph theory, in Combinatorics, Paul Erdős is Eighty, Vol. II (D. Miklós, V.T. Sos, and T. Szőnyi, eds.), 295–352, János Bolyai. Mathematical Society, Budapest.
    • (1996) Combinatorics, Paul Erdős is Eighty , vol.2 , pp. 295-352
    • Komlós, J.1    Simomovits, M.2
  • 65
    • 0000571438 scopus 로고
    • Über reihen mit positive gliedern
    • Knopp, K. (1928). Über Reihen mit positive Gliedern, J. London Math. Soc., 3, 205–211.
    • (1928) J. London Math. Soc , vol.3 , pp. 205-211
    • Knopp, K.1
  • 66
    • 0043275420 scopus 로고
    • Solutions analytiques de quelques problèmes sur les pyramides triangulaires
    • Lagrange, J. (1773). Solutions analytiques de quelques problèmes sur les pyramides triangulaires, Acad. Sci. Berlin.
    • (1773) Acad. Sci. Berlin
    • Lagrange, J.1
  • 67
    • 0010747076 scopus 로고
    • Über einen konvergenzsatz
    • Landau, E. (1907). Über einen Konvergenzsatz, Göttinger Nachrichten, 25–27.
    • (1907) Göttinger Nachrichten , pp. 25-27
    • Landau, E.1
  • 69
    • 84923177710 scopus 로고    scopus 로고
    • Technical Report, Department of Mathematics, Kwangwoon University, Seoul, Korea
    • Lee, H. (2002). Note on Muirhead’s Theorem, Technical Report, Department of Mathematics, Kwangwoon University, Seoul, Korea.
    • (2002) Note on Muirhead’s Theorem
    • Lee, H.1
  • 70
    • 84923122103 scopus 로고
    • (B. Bollobás, ed.), Cambridge University Press, Cambridge, UK
    • Littlewood, J.E. (1988). Littlewood’s Miscellany (B. Bollobás, ed.), Cambridge University Press, Cambridge, UK.
    • (1988) Littlewood’s Miscellany
    • Littlewood, J.E.1
  • 71
    • 0038363049 scopus 로고
    • North-Holland Mathematics Studies, Annals of Discrete Mathematics, Elsevier Science Publishers, Amsterdam, and Akadémiai Kiadó, Budapest
    • Lovász, L. and Plummer M.D. (1986). Matching Theory, North-Holland Mathematics Studies, Annals of Discrete Mathematics, vol. 29, Elsevier Science Publishers, Amsterdam, and Akadémiai Kiadó, Budapest.
    • (1986) Matching Theory , vol.29
    • Lovász, L.1    Plummer, M.D.2
  • 73
    • 0040664706 scopus 로고
    • Inequalities related to carleman’s inequality
    • (W.N. Everitt, ed.), Chapter 8, Marcel Decker, New York
    • Love, E.R. (1991). Inequalities related to Carleman’s inequality, in Inequalities: Fifty Years on from Hardy, Littlewood, and Pólya(W.N. Everitt, ed.), Chapter 8, Marcel Decker, New York.
    • (1991) In
    • Love, E.R.1
  • 74
    • 0004057512 scopus 로고
    • (translated from the 1st Russian edition, 1956, by D.L. Barnett), D.C. Heath and Company, Boston
    • Lyusternik, L.A. (1966). Convex Figures and Polyhedra (translated from the 1st Russian edition, 1956, by D.L. Barnett), D.C. Heath and Company, Boston.
    • (1966) Convex Figures and Polyhedra
    • Lyusternik, L.A.1
  • 76
    • 0142233350 scopus 로고
    • A second letter to martin folkes, esq.; concerning the roots of equations, with the demonstration of other rules in algebra
    • Maclaurin, C. (1729). A second letter to Martin Folkes, Esq.; concerning the roots of equations, with the demonstration of other rules in algebra, Phil. Transactions, 36, 59–96.
    • (1729) Phil. Transactions , vol.36 , pp. 59-96
    • Maclaurin, C.1
  • 78
    • 0006658738 scopus 로고    scopus 로고
    • Why hölder’s inequality should be called rogers’ inequality
    • Maligranda, L. (1998). Why Hölder’s inequality should be called Rogers’ inequality, Mathematical Inequalities and Applications, 1, 69–83.
    • (1998) Mathematical Inequalities and Applications , vol.1 , pp. 69-83
    • Maligranda, L.1
  • 79
    • 0347603188 scopus 로고    scopus 로고
    • Equivalence of the hölder–rogers andminkowski inequalities
    • Maligranda, L. (2000). Equivalence of the Hölder–Rogers andMinkowski inequalities, Mathematical Inequalities and Applications, 4, 203–207.
    • (2000) Mathematical Inequalities and Applications , vol.4 , pp. 203-207
    • Maligranda, L.1
  • 80
    • 0011649824 scopus 로고
    • On clarkson’s inequalities and interpolation
    • Maligranda, L. and Persson, L.E (1992). On Clarkson’s inequalities and interpolation, Math. Nachr., 155, 187–197.
    • (1992) Math. Nachr , vol.155 , pp. 187-197
    • Maligranda, L.1    Persson, L.E.2
  • 81
    • 0040156918 scopus 로고
    • Inequalities and interpolation
    • Maligranda, L. and Persson, L.E (1993). Inequalities and Interpolation, Collect. Math., 44, 181–199.
    • (1993) Collect. Math , vol.44 , pp. 181-199
    • Maligranda, L.1    Persson, L.E.2
  • 82
    • 85199154514 scopus 로고    scopus 로고
    • Princeton University Press, Princeton, NJ
    • Maor, E. (1998). Trigonometric Delights, Princeton University Press, Princeton, NJ.
    • (1998) Trigonometric Delights
    • Maor, E.1
  • 84
    • 60349130337 scopus 로고    scopus 로고
    • Problem number 10944
    • Mazur, M. (2002). Problem Number 10944, Amer. Math. Monthly, 109, 475.
    • (2002) Amer. Math. Monthly , vol.109 , pp. 475
    • Mazur, M.1
  • 86
    • 0003175889 scopus 로고
    • Sur les séries de fonctions orthogonales (Première partie)
    • Menchoff, D. (1923). Sur les séries de fonctions orthogonales (première partie), Fundamenta Mathematicae, 4, 82–105.
    • (1923) Fundamenta Mathematicae , vol.4 , pp. 82-105
    • Menchoff, D.1
  • 88
    • 21944442437 scopus 로고    scopus 로고
    • On the extended hilbert’s inequality
    • Mingzhe, G. and Bichen, Y. (1998). On the extended Hilbert’s inequality, Proc. Amer. Math. Soc., 126, 751–759.
    • (1998) Proc. Amer. Math. Soc , vol.126 , pp. 751-759
    • Mingzhe, G.1    Bichen, Y.2
  • 89
    • 40049093761 scopus 로고
    • History, variations and generalizations of the čebyˇsev inequality and the question of some priorities
    • Mitrinović, D.S. and Vasić, P.M. (1974). History, variations and generalizations of the čebyˇsev inequality and the question of some priorities, Univ. Beograd Publ. Electrotehn. Fak. Ser. Mat. Fiz., 461, 1–30.
    • (1974) Univ. Beograd Publ. Electrotehn. Fak. Ser. Mat. Fiz , vol.461 , pp. 1-30
    • Mitrinović, D.S.1    Vasić, P.M.2
  • 92
    • 0002314229 scopus 로고
    • The arithmetic-geometric inequality
    • O. Shisha, ed.), Academic Press, Boston
    • Motzkin, T.S. (1967). The arithmetic-geometric inequality, in Inequalities (O. Shisha, ed.), 483–489, Academic Press, Boston.
    • (1967) Inequalities , pp. 483-489
    • Motzkin, T.S.1
  • 93
    • 84923132685 scopus 로고    scopus 로고
    • Solution of a problem 10940 proposed by y. Nievergelt
    • Nakhash, A. (2003). Solution of a Problem 10940 proposed by Y. Nievergelt, Amer. Math. Monthly, 110, 546–547.
    • (2003) Amer. Math. Monthly , vol.110 , pp. 546-547
    • Nakhash, A.1
  • 97
    • 84972544002 scopus 로고
    • On the definition of normal numbers
    • Niven, I. and Zuckerman, H.S. (1951). On the definition of normal numbers, Pacific J. Math., 1, 103–109.
    • (1951) Pacific J. Math , vol.1 , pp. 103-109
    • Niven, I.1    Zuckerman, H.S.2
  • 98
    • 84923194609 scopus 로고    scopus 로고
    • Problem 10940 the complex geometric mean
    • Nivergelt, Y. (2002). Problem 10940 The complex geometric mean, Amer. Math. Monthly, 109, 393.
    • (2002) Amer. Math. Monthly , vol.109 , pp. 393
    • Nivergelt, Y.1
  • 99
    • 84918295731 scopus 로고
    • Inequalities among averages
    • Norris, N. (1935). Inequalities among averages, Ann. Math. Statistics, 6, 27–29.
    • (1935) Ann. Math. Statistics , vol.6 , pp. 27-29
    • Norris, N.1
  • 100
    • 26444607540 scopus 로고
    • An elementary proof of hilbert’s inequality
    • Oleszkiewicz, K. (1993). An elementary proof of Hilbert’s inequality, Amer. Math. Monthly, 100, 276–280.
    • (1993) Amer. Math. Monthly , vol.100 , pp. 276-280
    • Oleszkiewicz, K.1
  • 103
  • 105
    • 0005447577 scopus 로고    scopus 로고
    • Carleman’s inequality: History and new generalizations
    • Pečarić, J.E. and Stolarsky, K.B. (2001). Carleman’s inequality: history and new generalizations, Aequationes Math., 61, 49–62.
    • (2001) Aequationes Math , vol.61 , pp. 49-62
    • Pečarić, J.E.1    Stolarsky, K.B.2
  • 106
    • 0004256568 scopus 로고    scopus 로고
    • Springer-Verlag, Berlin
    • Pitman, J. (1997). Probability, Springer-Verlag, Berlin.
    • (1997) Probability
    • Pitman, J.1
  • 107
    • 84860032273 scopus 로고
    • Proof of an inequality
    • Pólya, G. (1926). Proof of an inequality, Proc. London Math. Soc., 24, 57.
    • (1926) Proc. London Math. Soc , vol.24 , pp. 57
    • Pólya, G.1
  • 108
    • 0038360436 scopus 로고
    • With, or without, motivation
    • Pólya, G. (1949). With, or without, motivation, Amer. Math. Monthly, 56, 684–691, 1949.
    • (1949) Amer. Math. Monthly , vol.56 , pp. 684-691
    • Pólya, G.1
  • 109
    • 0013161523 scopus 로고
    • On the harmonic mean of two numbers
    • Pólya, G. (1950). On the harmonic mean of two numbers, Amer. Math. Monthly, 57, 26–28.
    • (1950) Amer. Math. Monthly , vol.57 , pp. 26-28
    • Pólya, G.1
  • 111
    • 0004235832 scopus 로고
    • 2nd edition, Princeton University Press, Princeton, NJ
    • Polya, G. (1957). How to Solve It, 2nd edition, Princeton University Press, Princeton, NJ.
    • (1957) How to Solve It
    • Polya, G.1
  • 113
    • 34250957541 scopus 로고
    • Einige sätze Über reihen von allgemeinen orthogonal funktionen
    • Rademacher, H. (1922). Einige Sätze Über Reihen von allgemeinen Orthogonal funktionen, Math. Annalen, 87, 112–138.
    • (1922) Math. Annalen , vol.87 , pp. 112-138
    • Rademacher, H.1
  • 114
    • 0040402782 scopus 로고
    • London Mathematical Lecture Series, Cambridge University Press, Cambridge, UK
    • Rajwade, A.R. (1993). Squares, London Mathematical Lecture Series, 171, Cambridge University Press, Cambridge, UK.
    • (1993) Squares , vol.171
    • Rajwade, A.R.1
  • 115
    • 84923188450 scopus 로고
    • Hardy’s inequality for geometric series (Solution of a problem by walther janous)
    • Richberg, R. (1993). Hardy’s inequality for geometric series (solution of a problem by Walther Janous), Amer. Math. Monthly, 100, 592–593.
    • (1993) Amer. Math. Monthly , vol.100 , pp. 592-593
    • Richberg, R.1
  • 116
    • 84889966296 scopus 로고
    • Sur les suites de fonctions mesurables
    • Riesz, F. (1909). Sur les suites de fonctions mesurables, C. R. Acad. Sci. Paris, 148, 1303–1305.
    • (1909) C. R. Acad. Sci. Paris , vol.148 , pp. 1303-1305
    • Riesz, F.1
  • 117
    • 0000732178 scopus 로고
    • Untersuchungen Über systeme integrierbare funktionen
    • Riesz, F. (1910). Untersuchungen Über Systeme integrierbare Funktionen, Math. Annalen, 69, 449–497.
    • (1910) Math. Annalen , vol.69 , pp. 449-497
    • Riesz, F.1
  • 118
    • 51649133409 scopus 로고
    • Sur les maxima des formes bilinéaires et sur les fonctionnelles linéaires
    • Riesz, M. (1927). Sur les maxima des formes bilinéaires et sur les fonctionnelles linéaires, Acta Math., 49, 465–487.
    • (1927) Acta Math , vol.49 , pp. 465-487
    • Riesz, M.1
  • 120
    • 0010300426 scopus 로고
    • An extension of a certain theorem in inequalities
    • Rogers, L.J. (1888). An extension of a certain theorem in inequalities, Messenger of Math., 17, 145–150.
    • (1888) Messenger of Math , vol.17 , pp. 145-150
    • Rogers, L.J.1
  • 121
    • 0005494621 scopus 로고
    • Normalized symmetric functions, newton’s inequalities, and a new set of stronger inequalities
    • Rosset, S. (1989). Normalized symmetric functions, Newton’s inequalities, and a new set of stronger inequalities, Amer. Math. Monthly, 96, 815–819.
    • (1989) Amer. Math. Monthly , vol.96 , pp. 815-819
    • Rosset, S.1
  • 123
    • 0034345770 scopus 로고    scopus 로고
    • Sums of squares of polynomials
    • Rudin, W. (2000). Sums of Squares of Polynomials, Amer. Math. Monthly, 107, 813–821.
    • (2000) Amer. Math. Monthly , vol.107 , pp. 813-821
    • Rudin, W.1
  • 124
    • 84943488562 scopus 로고
    • Bemerkungen zur theorie der beschränkten bilinearformen mit unendlich vielen veränderlichen
    • Schur, I. (1911). Bemerkungen zur Theorie der beschränkten Bilinearformen mit unendlich vielen Veränderlichen, J. Mathematik, 140, 1–28.
    • (1911) J. Mathematik , vol.140 , pp. 1-28
    • Schur, I.1
  • 126
    • 0039820479 scopus 로고
    • Über ein die flächen kleinsten flächeninhalts betreffendes problem der variationsrechnung
    • Schwarz, H.A. (1885). Über ein die Flächen kleinsten Flächeninhalts betreffendes Problem der Variationsrechnung. Acta Soc. Scient. Fenn., 15, 315–362.
    • (1885) Acta Soc. Scient. Fenn , vol.15 , pp. 315-362
    • Schwarz, H.A.1
  • 128
    • 84923134216 scopus 로고
    • An application of schwarz inequality
    • Sigillito, V.G. (1968). An application of Schwarz inequality, Amer. Math. Monthly, 75, 656–658.
    • (1968) Amer. Math. Monthly , vol.75 , pp. 656-658
    • Sigillito, V.G.1
  • 129
    • 18444413037 scopus 로고    scopus 로고
    • Exponential sums in coding theory, cryptology, and algorithms
    • H. Niederreiter, ed.), Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, World Scientific Publishing, Singapore
    • Shparlinski, I.E. (2002). Exponential Sums in Coding Theory, Cryptology, and Algorithms, in Coding Theory and Cryptology (H. Niederreiter, ed.), Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, Vol. I., World Scientific Publishing, Singapore.
    • (2002) Coding Theory and Cryptology , vol.1
    • Shparlinski, I.E.1
  • 130
    • 0003998919 scopus 로고
    • (Notes by B. Friedman rewritten by K. Chandrasekharan with assistance of R. Suter), Springer-Verlag, Berlin
    • Siegel, C.L. (1989). Lectures on the Geometry of Numbers (Notes by B. Friedman rewritten by K. Chandrasekharan with assistance of R. Suter), Springer-Verlag, Berlin.
    • (1989) Lectures on the Geometry of Numbers
    • Siegel, C.L.1
  • 131
    • 63449094182 scopus 로고
    • On a generalization of the cauchy–schwarz inequality
    • Steiger, W. L. (1969). On a generalization of the Cauchy–Schwarz inequality, Amer. Math. Monthly, 76, 815–816.
    • (1969) Amer. Math. Monthly , vol.76 , pp. 815-816
    • Steiger, W.L.1
  • 132
    • 84923177706 scopus 로고
    • Lösung eine aufgabe von g. Pólya
    • Ser. 3
    • Szegő, G. (1914). Lösung eine Aufgabe von G. Pólya, Archiv für Mathematik u. Physik, Ser. 3, 22, 361–362.
    • (1914) Archiv für Mathematik U. Physik , Issue.22 , pp. 361-362
    • Szegő, G.1
  • 135
    • 33750558940 scopus 로고
    • Zur theorie der quadratischen formen von unendlische vielen veränderlichen
    • Toeplitz, O. (1910). Zur Theorie der quadratischen Formen von unendlische vielen Veränderlichen, Göttinger Nach., 489–506.
    • (1910) Göttinger Nach , pp. 489-506
    • Toeplitz, O.1
  • 137
  • 139
    • 0041957594 scopus 로고
    • A rearrangement inequality and the permutahedron
    • Vince, A. (1990). A rearrangement inequality and the permutahedron, Amer. Math. Monthly, 97, 319–323.
    • (1990) Amer. Math. Monthly , vol.97 , pp. 319-323
    • Vince, A.1
  • 141
    • 72049132983 scopus 로고
    • Do symmetric problems have symmetric solutions?
    • Waterhouse, W. (1983). Do symmetric problems have symmetric solutions? Amer. Math. Monthly, 90, 378–387.
    • (1983) Amer. Math. Monthly , vol.90 , pp. 378-387
    • Waterhouse, W.1
  • 142
    • 34250956128 scopus 로고
    • Über die konvergenz von reihen, die nach orthogonalfunktionen fortschreiten
    • Weyl, H. (1909). Über die Konvergenz von Reihen, die nach Orthogonalfunktionen fortschreiten, Math. Ann., 67, 225–245.
    • (1909) Math. Ann , vol.67 , pp. 225-245
    • Weyl, H.1
  • 143
    • 0037960194 scopus 로고
    • Über die gleichverteilung von zahlen mod eins
    • Weyl, H. (1916). Über die Gleichverteilung von Zahlen mod Eins, Math. Ann., 77, 312–352.
    • (1916) Math. Ann , vol.77 , pp. 312-352
    • Weyl, H.1
  • 144
    • 0347346894 scopus 로고
    • Almost periodic invariant vector sets in a metric vector space
    • Weyl, H. (1949). Almost periodic invariant vector sets in a metric vector space, Amer. J. Math., 71, 178–205.
    • (1949) Amer. J. Math , vol.71 , pp. 178-205
    • Weyl, H.1
  • 145
    • 84966200544 scopus 로고
    • Some applications of the inequality of arithmetic and geometric means to polynomial equations
    • Wilf, H.S. (1963). Some applications of the inequality of arithmetic and geometric means to polynomial equations, Proc. Amer. Math. Soc., 14, 263–265.
    • (1963) Proc. Amer. Math. Soc , vol.14 , pp. 263-265
    • Wilf, H.S.1
  • 146
    • 0010997441 scopus 로고
    • Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, Berlin
    • Wilf, H.S. (1970). Finite Sections of Some Classical Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, 52, Springer-Verlag, Berlin.
    • (1970) Finite Sections of Some Classical Inequalities , vol.52
    • Wilf, H.S.1
  • 148
    • 51249193142 scopus 로고
    • Diophantische ungleichungen i. Zur gleicheverteilung modulo eins
    • van der Corput, J.G. (1931). Diophantische Ungleichungen I. Zur Gleicheverteilung Modulo Eins, Acta Math., 56, 373–456.
    • (1931) Acta Math , vol.56 , pp. 373-456
    • Van Der Corput, J.G.1
  • 149
    • 0004148171 scopus 로고
    • (translated by Saul Kravetz from the 5th revised Russian edition, 1949), Dover Publications, New York
    • Vinogradov, I.M. (1954). Elements of Number Theory (translated by Saul Kravetz from the 5th revised Russian edition, 1949), Dover Publications, New York.
    • (1954) Elements of Number Theory
    • Vinogradov, I.M.1


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