On l'Hospital-type rules for monotonicity

Journal of Inequalities in Pure and Applied Mathematics

Volumn 7, Issue 2, 2006, Pages 1-19

  Pinelis, Iosif ^a  

^a MICHIGAN TECHNOLOGICAL UNIVERSITY   (United States)

Author keywords

Anderson Vamanamurthy Vuorinen inequalities; Becker Stark inequalities; Borwein Borwein Rooin ratio; Hyperbolic geometry; L'Hospital type rules; Log concavity; Maclaurin series; Monotonicity; Right angled triangles

Indexed keywords

EID: 33744742239     PISSN: 14435756     EISSN: 14435756     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. G.D. ANDERSON, S.-L. QIU, M.K. VAMANAMURTHY AND M. VUORINEN, Generalized elliptic integrals and modular equations, Pacific J. Math., 192 (2000), 1-37.
2. G.D. ANDERSON, M.K. VAMANAMURTHY, AND M. VUORINEN, Inequalities for quasiconformal mappings in space, Pacific J. Math., 160 (1993), 1-18.
3. G.D. ANDERSON, M.K. VAMANAMURTHY, AND M. VUORINEN, Conformal Invariants, Inequalities, and Quasiconformal Maps, Wiley, New York 1997.
4. G.D. ANDERSON, M.K. VAMANAMURTHY, AND M. VUORINEN, Topics in special functions, Papers on Analysis, Rep. Univ. Jyväskylä Dep. Math. Stat., Vol. 83, Univ. Jyväskylä, Jyväskylä, 2001, pp. 5-26.
5. G.D. ANDERSON, M.K. VAMANAMURTHY AND M. VUORINEN, Monotonicity rules in calculus, Amer. Math. Monthly, to appear.
6. T.M. APOSTOL, Mathematical Analysis: A Modern Approach to Advanced Calculus, Second Ed., Addison-Wesley, Reading, MA 1975.
7. A.F. BEARDON, The Geometry of Discrete Groups, Graduate Texts in Mathematics, Vol. 91. Springer-Verlag, New York, 1983.
8. M. BECKER AND E.L. STARK, On a hierarchy of quolynomial inequalities for tan x, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., No. 602-633 (1978), 133-138.
9. D. BORWEIN, J.M. BORWEIN, J. ROOIN AND J. GRIEVAUX, Convex and concave functions, Amer. Math. Monthly, 112 (2005), 92-93.
10. I. CHAVEL, Riemannian Geometry - A Modern Introduction, Cambridge Univ. Press, Cambridge, 1993.
11. J. CHEEGER, M. GROMOV, AND M. TAYLOR, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Diff. Geom., 17 (1982), 15-54.
12. M. GROMOV, Isoperimetric inequalities in Riemannian manifolds, Asymptotic Theory of Finite Dimensional Spaces, Lecture Notes Math., vol. 1200, Appendix I, Springer, Berlin, 1986, pp. 114-129.
13. 2 test under symmetry condition, Preprint, 1991. A shorter version of the preprint appeared in Ann. Statist., 22 (1994), 357-368.
14. I. PINELIS, Fractional sums and integrals of r-concave tails and applications to comparison probability inequalities, Advances In Stochastic Inequalities (Atlanta, GA, 1997), 149-168,
15. Contemp. Math., 234, Amer. Math. Soc., Providence, RI, 1999.
16. I. PINELIS, L'Hospital type results for monotonicity, with applications, J. Inequal. Pure Appl. Math., 3(1) (2002), Art. 5, 5 pp. [ONLINE: http://jipam.vu.edu.au/article.php?sid=158].
17. I. PINELIS, L'Hospital type rules for oscillation, with applications, J. Inequal. Pure Appl. Math., 2(3) (2001), Art. 33, 24pp. [ONLINE: http://jipam.vu.edu.au/article.php?sid=149].
18. I. PINELIS, Monotonicity properties of the relative error of a Padé approximation for Mills' ratio, J. Inequal. Pure Appl. Math., 3(2) (2002), Art. 20, 8 pp. [ONLINE: http://jipam.vu.edu.au/article.php?sid=172].
19. I. PINELIS, L'Hospital type rules for monotonicity: applications to probability inequalities for sums of bounded random variables, J. Inequal. Pure Appl. Math., 3(1) (2002), Art. 7, 9 pp. [ONLINE: http://jipam.vu.edu.au/article. php?sid=160].
20. I. PINELIS, L'Hospital rules for monotonicity and the Wilker-Anglesio inequality, Amer. Math. Monthly, 111 (2004) 905-909.
21. I. PINELIS, L'Hospital-type rules for monotonicity and limits: discrete case, Preprint, 2005.
22. I. PINELIS, L'Hospital-type Rules for monotonicity, and the Lambert and Saccheri quadrilaterals in hyperbolic geometry, J. Inequal. Pure Appl. Math., 6(4) (2005), Art. 99, 12 pp. [ONLINE: http://jipam.vu.edu.au/article.php?sid= 573].
23. E.C. TITCHMARSH, The Theory of Functions, Second Ed., Oxford Univ. Press, London, 1939.