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Volumn 1693, Issue , 2008, Pages 1-238

From Hahn-Banach to Monotonicity

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EID: 85072855841     PISSN: 00758434     EISSN: 16179692     Source Type: Book Series    
DOI: 10.1007/BFb0093634     Document Type: Chapter
Times cited : (70)

References (122)
  • 2
    • 0000208446 scopus 로고    scopus 로고
    • Somme ponctuelle d’opérateurs max-imaux monotones
    • H. Attouch, H. Riahi and M. Théra, Somme ponctuelle d’opérateurs max-imaux monotones, Serdica Math. J. 22 (1996), 267–292.
    • (1996) Serdica Math. J. , vol.22 , pp. 267-292
    • Attouch, H.1    Riahi, H.2    Théra, M.3
  • 3
    • 0004002220 scopus 로고
    • Wiley, New York – Chichester – Brisbane – Toronto – Singapore
    • J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley, New York – Chichester – Brisbane – Toronto – Singapore (1984).
    • (1984) Applied Nonlinear Analysis
    • Aubin, J.-P.1    Ekeland, I.2
  • 5
    • 33845366887 scopus 로고    scopus 로고
    • Fitzpatrick functions, cyclic monotonicity and Rockafellar’s antiderivative
    • S. Bartz, H. H. Bauschke, J. M. Borwein, S. Reich and X. Wang, Fitzpatrick functions, cyclic monotonicity and Rockafellar’s antiderivative, Nonlinear Anal. 66 (2007), 1198–1223.
    • (2007) Nonlinear Anal , vol.66 , pp. 1198-1223
    • Bartz, S.1    Bauschke, H.H.2    Borwein, J.M.3    Reich, S.4    Wang, X.5
  • 7
    • 34250724621 scopus 로고    scopus 로고
    • Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings
    • H. H. Bauschke, Fenchel duality, Fitzpatrick functions and the extension of firmly nonexpansive mappings, Proc. Amer. Math. Soc. 135 (2007), 135–139.
    • (2007) Proc. Amer. Math. Soc. , vol.135 , pp. 135-139
    • Bauschke, H.H.1
  • 9
    • 0012677529 scopus 로고    scopus 로고
    • Maximal monotonicity of dense type, local maximal monotonicity, and monotonicity of the conjugate are all the same for continuous linear operators
    • H. H. Bauschke and J. M. Borwein, Maximal monotonicity of dense type, local maximal monotonicity, and monotonicity of the conjugate are all the same for continuous linear operators, Pacific J. Math. 189 (1999), 1–20.
    • (1999) Pacific J. Math , vol.189 , pp. 1-20
    • Bauschke, H.H.1    Borwein, J.M.2
  • 11
    • 0033177392 scopus 로고    scopus 로고
    • Stronger maximal monotonicity properties of linear operators
    • H. H. Bauschke and S. Simons, Stronger maximal monotonicity properties of linear operators, Bull. Austral. Math. Soc. 60 (1999), 163–174.
    • (1999) Bull. Austral. Math. Soc. , vol.60 , pp. 163-174
    • Bauschke, H.H.1    Simons, S.2
  • 12
    • 33846522955 scopus 로고    scopus 로고
    • Fitzpatrick functions: Inequalities, examples, and remarks on a problem by S. Fitzpatrick
    • H. H. Bauschke, D. A. McLaren and H. S. Sendov, Fitzpatrick functions: inequalities, examples, and remarks on a problem by S. Fitzpatrick, J. Convex Anal. 13 (2006), 499–523.
    • (2006) J. Convex Anal. , vol.13 , pp. 499-523
    • Bauschke, H.H.1    McLaren, D.A.2    Sendov, H.S.3
  • 14
    • 38249008267 scopus 로고
    • The slice topology: A viable alternative to Mosco convergence in nonreflexive spaces
    • G. Beer, The slice topology: A viable alternative to Mosco convergence in nonreflexive spaces, Nonlinear Anal. 19 (1992), 271–290.
    • (1992) Nonlinear Anal , vol.19 , pp. 271-290
    • Beer, G.1
  • 16
    • 0012860804 scopus 로고
    • A Lagrange multiplier theorem and a sandwich theorem for convex relations
    • J. M. Borwein, A Lagrange multiplier theorem and a sandwich theorem for convex relations, Math. Scand. 48 (1981), 198–204.
    • (1981) Math. Scand. , vol.48 , pp. 198-204
    • Borwein, J.M.1
  • 17
    • 33749528052 scopus 로고    scopus 로고
    • Maximal monotonicity via convex analysis
    • J. M. Borwein, Maximal monotonicity via convex analysis, J. Convex Anal. 13 (2006), 561–586.
    • (2006) J. Convex Anal. , vol.13 , pp. 561-586
    • Borwein, J.M.1
  • 18
    • 43049170879 scopus 로고    scopus 로고
    • Maximality of sums of two maximal monotone operators in general Banach space
    • J. M. Borwein, Maximality of sums of two maximal monotone operators in general Banach space, Proc. Amer. Math. Soc. 135 (2007), 3917–3924.
    • (2007) Proc. Amer. Math. Soc. , vol.135 , pp. 3917-3924
    • Borwein, J.M.1
  • 19
    • 59649105932 scopus 로고    scopus 로고
    • Simon Fitzpatrick memorial volume
    • J. M. Borwein et al., Simon Fitzpatrick memorial volume, J. Convex Anal. 13 (2006), 463–476.
    • (2006) J. Convex Anal. , vol.13 , pp. 463-476
    • Borwein, J.M.1
  • 21
    • 84973937890 scopus 로고
    • Local boundedness of monotone operators under minimal hypotheses
    • J. M. Borwein and S. Fitzpatrick, Local boundedness of monotone operators under minimal hypotheses, Bull. Austral. Math. Soc. 39 (1988), 439–441.
    • (1988) Bull. Austral. Math. Soc. , vol.39 , pp. 439-441
    • Borwein, J.M.1    Fitzpatrick, S.2
  • 22
    • 0002395296 scopus 로고
    • Examples of convex functions and classification of normed spaces
    • J. Borwein, S. Fitzpatrick and J. Vanderwerff, Examples of convex functions and classification of normed spaces, J. Convex Anal. 1 (1994), 61–73.
    • (1994) J. Convex Anal. , vol.1 , pp. 61-73
    • Borwein, J.1    Fitzpatrick, S.2    Vanderwerff, J.3
  • 25
    • 34250743164 scopus 로고    scopus 로고
    • A new condition for maximal monotonicity via representative functions
    • R. I. Boţ, E. R. Csetnek and G. Wanka, A new condition for maximal monotonicity via representative functions, Nonlinear Anal. 67 (2007), 2390–2402.
    • (2007) Nonlinear Anal , vol.67 , pp. 2390-2402
    • Boţ, R.I.1    Csetnek, E.R.2    Wanka, G.3
  • 26
    • 36248962713 scopus 로고    scopus 로고
    • Maximal monotonicity for the pre-composition with a linear operator
    • R. I. Boţ, S.–M. Grad and G. Wanka, Maximal monotonicity for the pre-composition with a linear operator, Siam J. Optim. 17 (2007), 1239–1252.
    • (2007) Siam J. Optim. , vol.17 , pp. 1239-1252
    • Boţ, R.I.1    Grad, S.–.M.2    Wanka, G.3
  • 27
    • 33645961296 scopus 로고    scopus 로고
    • A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces
    • R. I. Boţ and G. Wanka, A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces, Nonlinear Anal. 64 (2006), 2787–2804.
    • (2006) Nonlinear Anal , vol.64 , pp. 2787-2804
    • Boţ, R.I.1    Wanka, G.2
  • 29
    • 84980140308 scopus 로고
    • Perturbations of nonlinear maximal monotone sets in Banach spaces
    • H. Brezis, M. G. Crandall and A. Pazy, Perturbations of nonlinear maximal monotone sets in Banach spaces, Comm. Pur. Appl. Math. 23 (1970), 123– 144.
    • (1970) Comm. Pur. Appl. Math. , vol.23 , pp. 123-144
    • Brezis, H.1    Crandall, M.G.2    Pazy, A.3
  • 30
    • 51249191056 scopus 로고
    • Image d’une somme d’opérateurs monotone et applications
    • H. Brezis and A. Haraux, Image d’une somme d’opérateurs monotone et applications, Israel J. Math. 23 (1976), 165–186.
    • (1976) Israel J. Math. , vol.23 , pp. 165-186
    • Brezis, H.1    Haraux, A.2
  • 31
    • 84968503350 scopus 로고
    • On the Subdifferentiability of Convex Functions
    • A. Brøndsted and R.T. Rockafellar, On the Subdifferentiability of Convex Functions, Proc. Amer. Math. Soc. 16 (1965), 605–611.
    • (1965) Proc. Amer. Math. Soc. , vol.16 , pp. 605-611
    • Brøndsted, A.1    Rockafellar, R.T.2
  • 32
    • 34250511959 scopus 로고
    • Nonlinear maximal monotone operators in Banach spaces
    • F. E. Browder, Nonlinear maximal monotone operators in Banach spaces, Math. Annalen 175 (1968), 89–113.
    • (1968) Math. Annalen , vol.175 , pp. 89-113
    • Browder, F.E.1
  • 33
    • 0042745499 scopus 로고    scopus 로고
    • Maximal monotonicity, conjugation and the duality product
    • R. S. Burachik and B. F. Svaiter, Maximal monotonicity, conjugation and the duality product, Proc. Amer. Math. Soc. 131 (2003), 2379–2383.
    • (2003) Proc. Amer. Math. Soc. , vol.131 , pp. 2379-2383
    • Burachik, R.S.1    Svaiter, B.F.2
  • 34
    • 33644528747 scopus 로고    scopus 로고
    • Necessary and Sufficient Conditions for Stable Conjugate Duality
    • R. S. Burachik, V. Jeyakumar and Z-Y. Wu, Necessary and Sufficient Conditions for Stable Conjugate Duality, Nonlinear Anal. 64 (2006), 1998– 2006.
    • (2006) Nonlinear Anal , vol.64 , pp. 1998-2006
    • Burachik, R.S.1    Jeyakumar, V.2    Wu, Z.-Y.3
  • 35
    • 0006562511 scopus 로고    scopus 로고
    • On the sum of monotone operators
    • L.-J. Chu, On the sum of monotone operators, Michigan Math. J., 43 (1996), 273–289.
    • (1996) Michigan Math. J. , vol.43 , pp. 273-289
    • Chu, L.-J.1
  • 37
    • 0039926123 scopus 로고    scopus 로고
    • The convex function determined by a multifunction
    • M. Coodey and S. Simons, The convex function determined by a multifunction, Bull. Austral. Math. Soc. 54 (1996), 87–97.
    • (1996) Bull. Austral. Math. Soc. , vol.54 , pp. 87-97
    • Coodey, M.1    Simons, S.2
  • 38
    • 0003742468 scopus 로고
    • Springer–Verlag, New York – Heidelberg – Berlin – Tokyo
    • K. Deimling, Nonlinear Functional Analysis, Springer–Verlag, New York – Heidelberg – Berlin – Tokyo (1985).
    • (1985) Nonlinear Functional Analysis
    • Deimling, K.1
  • 39
    • 84966198944 scopus 로고
    • Nonconvex minimization problems
    • I. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. 1 (1979), 443–474.
    • (1979) Bull. Amer. Math. Soc. , vol.1 , pp. 443-474
    • Ekeland, I.1
  • 41
    • 84968466495 scopus 로고
    • Systems of inequalities involving convex functions
    • K. Fan, I. Glicksberg and A. J. Hoffman, Systems of inequalities involving convex functions, Proc. Amer. Math. Soc. 8 (1957), 617–622.
    • (1957) Proc. Amer. Math. Soc. , vol.8 , pp. 617-622
    • Fan, K.1    Glicksberg, I.2    Hoffman, A.J.3
  • 42
    • 0038231522 scopus 로고    scopus 로고
    • Workshop/Miniconference on Functional Analysis and Optimization (Can-berra, 1988), Proc. Centre Math. Anal. Austral. Nat. Univ. 20, Austral. Nat. Univ., Canberra, 1988
    • S. Fitzpatrick, Representing monotone operators by convex functions, Workshop/Miniconference on Functional Analysis and Optimization (Can-berra, 1988), 59–65, Proc. Centre Math. Anal. Austral. Nat. Univ. 20, Austral. Nat. Univ., Canberra, 1988.
    • Representing Monotone Operators by Convex Functions , pp. 59-65
    • Fitzpatrick, S.1
  • 43
    • 33846557425 scopus 로고    scopus 로고
    • Simon Fitzpatrick memorial volume
    • Simon Fitzpatrick memorial volume, J. Convex Anal. 13 (2006), No. 3–4.
    • (2006) J. Convex Anal , vol.13 , pp. 3-4
  • 45
    • 0041116334 scopus 로고
    • Some properties of maximal monotone operators on nonreflexive Banach spaces
    • S. P. Fitzpatrick and R. R. Phelps, Some properties of maximal monotone operators on nonreflexive Banach spaces, Set–Valued Anal. 3 (1995), 51–69.
    • (1995) Set–Valued Anal , vol.3 , pp. 51-69
    • Fitzpatrick, S.P.1    Phelps, R.R.2
  • 46
    • 33746015298 scopus 로고    scopus 로고
    • On the pointwise maximum of convex functions
    • S. P. Fitzpatrick and S. Simons, On the pointwise maximum of convex functions, Proc. Amer. Math. Soc. 128 (2000), 3553–3561.
    • (2000) Proc. Amer. Math. Soc. , vol.128 , pp. 3553-3561
    • Fitzpatrick, S.P.1    Simons, S.2
  • 47
    • 77950668255 scopus 로고    scopus 로고
    • Maximal monotone operators are selfdual vector fields and vice-versa
    • in press
    • N. Ghoussoub, Maximal monotone operators are selfdual vector fields and vice-versa, Proc. Amer. Math. Soc., in press.
    • Proc. Amer. Math. Soc.
    • Ghoussoub, N.1
  • 48
    • 0001763991 scopus 로고
    • Opérateurs monotones non linéaires dans les espaces de Banach non réflexifs
    • J.-P. Gossez, Opérateurs monotones non linéaires dans les espaces de Banach non réflexifs, J. Math. Anal. Appl. 34 (1971), 371–395.
    • (1971) J. Math. Anal. Appl. , vol.34 , pp. 371-395
    • Gossez, J.-P.1
  • 49
    • 76649092579 scopus 로고
    • On the range of a coercive maximal monotone operator in a nonreflexive Banach space
    • J.-P. Gossez, On the range of a coercive maximal monotone operator in a nonreflexive Banach space, Proc. Amer. Math. Soc. 35 (1972), 88–92.
    • (1972) Proc. Amer. Math. Soc. , vol.35 , pp. 88-92
    • Gossez, J.-P.1
  • 50
    • 84966221444 scopus 로고
    • On a convexity property of the range of a maximal monotone operator
    • J.-P. Gossez, On a convexity property of the range of a maximal monotone operator, Proc. Amer. Math. Soc. 55 (1976), 359–360.
    • (1976) Proc. Amer. Math. Soc. , vol.55 , pp. 359-360
    • Gossez, J.-P.1
  • 51
    • 0003846949 scopus 로고
    • Geometric functional analysis and its applications
    • Springer–Verlag, New York – Heidelberg
    • R. B. Holmes, Geometric functional analysis and its applications, Graduate Texts in Mathematics 24 (1975), Springer–Verlag, New York – Heidelberg.
    • (1975) Graduate Texts in Mathematics 24
    • Holmes, R.B.1
  • 52
    • 85072857975 scopus 로고
    • I. Namioka, and co-authors, Linear Topological Spaces, D. Van Nostrand Co., Inc., Princeton – Toronto – London – Melbourne
    • J. L. Kelley, I. Namioka, and co-authors, Linear Topological Spaces, D. Van Nostrand Co., Inc., Princeton – Toronto – London – Melbourne (1963).
    • (1963)
    • Kelley, J.L.1
  • 53
    • 0001702789 scopus 로고
    • Über das Von Neumannsche Minimax-Theorem
    • H. König, Über das Von Neumannsche Minimax-Theorem, Arch. Math. 19 (1968), 482–487.
    • (1968) Arch. Math. , vol.19 , pp. 482-487
    • König, H.1
  • 54
    • 34250477659 scopus 로고
    • On certain applications of the Hahn–Banach and minimax theorems
    • H. König, On certain applications of the Hahn–Banach and minimax theorems, Arch. Math. 21 (1970), 583–591.
    • (1970) Arch. Math. , vol.21 , pp. 583-591
    • König, H.1
  • 55
    • 0007301729 scopus 로고
    • Sublineare Funktionale
    • H. König, Sublineare Funktionale, Arch. Math. 23 (1972), 500–508.
    • (1972) Arch. Math. , vol.23 , pp. 500-508
    • König, H.1
  • 56
    • 0040913553 scopus 로고
    • Some Basic Theorems in Convex Analysis
    • edited by B. Korte, North-Holland
    • H. König, Some Basic Theorems in Convex Analysis, in “Optimization and operations research”, edited by B. Korte, North-Holland (1982).
    • (1982) Optimization and Operations Research
    • König, H.1
  • 57
    • 53249132853 scopus 로고    scopus 로고
    • Maximal monotone operators in the one–dimensional case
    • S. Kum, Maximal monotone operators in the one–dimensional case, J. Korean Math. Soc. 34 (1997), 371–381.
    • (1997) J. Korean Math. Soc. , vol.34 , pp. 371-381
    • Kum, S.1
  • 58
    • 84875207093 scopus 로고    scopus 로고
    • A resolution of Simons’ maximal monotonicity problem
    • D. T. Luc, A resolution of Simons’ maximal monotonicity problem, J. Convex Anal. 3 (1996), 367–370.
    • (1996) J. Convex Anal. , vol.3 , pp. 367-370
    • Luc, D.T.1
  • 59
    • 0004098975 scopus 로고
    • John Wiley & Sons, Inc, New York – Chichester – Brisbane – Toronto – Singapore
    • D. L. Luenberger, Optimization by Vector Space Methods, John Wiley & Sons, Inc, New York – Chichester – Brisbane – Toronto – Singapore (1969).
    • (1969) Optimization by Vector Space Methods
    • Luenberger, D.L.1
  • 61
    • 18744404859 scopus 로고    scopus 로고
    • Monotone operators representable by l.S.c. convex functions
    • J–E. Martínez-Legaz and B. F. Svaiter, Monotone operators representable by l.s.c. convex functions, Set–Valued Anal. 13 (2005), 21–46.
    • (2005) Set–Valued Anal , vol.13 , pp. 21-46
    • Martínez-Legaz, J.–.E.1    Svaiter, B.F.2
  • 62
    • 0001388784 scopus 로고    scopus 로고
    • ε–Subdifferentials in terms of subdifferentials, Set–Valued
    • J.–E. Martínez-Legaz and M. Théra, ε–Subdifferentials in terms of subdifferentials, Set–Valued Anal. 4 (1996), 327–332.
    • (1996) Anal , vol.4 , pp. 327-332
    • Martínez-Legaz, J.–.E.1    Théra, M.2
  • 65
    • 0038249045 scopus 로고    scopus 로고
    • Autoconjugate functions and representations of monotone operators
    • J.–P. Penot, Autoconjugate functions and representations of monotone operators, Bull. Austral. Math. Soc. 67 (2003), 277–284.
    • (2003) Bull. Austral. Math. Soc. , vol.67 , pp. 277-284
    • Penot, J.–.P.1
  • 66
    • 4243129234 scopus 로고    scopus 로고
    • The relevance of convex analysis for the study of monotonicity
    • J.–P. Penot, The relevance of convex analysis for the study of monotonicity, Nonlinear Anal. 58 (2004), 855–871.
    • (2004) Nonlinear Anal , vol.58 , pp. 855-871
    • Penot, J.–.P.1
  • 67
    • 33745965189 scopus 로고    scopus 로고
    • Some problems about the representation of monotone operators by convex functions
    • J.–P. Penot and C. Zălinescu, Some problems about the representation of monotone operators by convex functions, ANZIAM J. 47 (2005), 1–20.
    • (2005) ANZIAM J , vol.47 , pp. 1-20
    • Penot, J.–.P.1    Zălinescu, C.2
  • 69
    • 0006554342 scopus 로고    scopus 로고
    • Lectures on Maximal Monotone Operators
    • R. R. Phelps, Lectures on Maximal Monotone Operators, Extracta Mathematicae 12 (1997), 193–230.
    • (1997) Extracta Mathematicae , vol.12 , pp. 193-230
    • Phelps, R.R.1
  • 70
    • 22444453086 scopus 로고    scopus 로고
    • Unbounded linear monotone operators on nonreflexive Banach spaces
    • R. R. Phelps and S. Simons, Unbounded linear monotone operators on nonreflexive Banach spaces, J. Convex Anal. 5 (1998), 303–328.
    • (1998) J. Convex Anal. , vol.5 , pp. 303-328
    • Phelps, R.R.1    Simons, S.2
  • 71
    • 84966202691 scopus 로고
    • Weak compactness in locally convex spaces
    • J. D. Pryce, Weak compactness in locally convex spaces, Proc. Amer. Math. Soc. 17 (1966), 148–155.
    • (1966) Proc. Amer. Math. Soc. , vol.17 , pp. 148-155
    • Pryce, J.D.1
  • 72
    • 0001578798 scopus 로고
    • The range of sums of accretive and monotone operators
    • S. Reich, The range of sums of accretive and monotone operators, J. Math. Anal. Appl. 68 (1979), 310–317.
    • (1979) J. Math. Anal. Appl. , vol.68 , pp. 310-317
    • Reich, S.1
  • 73
    • 24944580357 scopus 로고    scopus 로고
    • Fenchel duality, Fitzpatrick functions and the Kirszbraun-Valentine extension theorem
    • S. Reich and S. Simons, Fenchel duality, Fitzpatrick functions and the Kirszbraun-Valentine extension theorem, Proc. Amer. Math. Soc. 133 (2005), 2657–2660.
    • (2005) Proc. Amer. Math. Soc. , vol.133 , pp. 2657-2660
    • Reich, S.1    Simons, S.2
  • 74
    • 0036466442 scopus 로고    scopus 로고
    • Enlargements and sums of monotone operators
    • Ser. A
    • J. P. Revalski and M. Théra, Enlargements and sums of monotone operators, Nonlinear Anal. 48 (2002), Ser. A, 505–519.
    • (2002) Nonlinear Anal , vol.48 , pp. 505-519
    • Revalski, J.P.1    Théra, M.2
  • 75
    • 0016952838 scopus 로고
    • Regularity and stability for convex multivalued functions
    • S. M. Robinson, Regularity and stability for convex multivalued functions, Math. Oper. Res. 1 (1976), 130–143.
    • (1976) Math. Oper. Res. , vol.1 , pp. 130-143
    • Robinson, S.M.1
  • 76
    • 0002793794 scopus 로고
    • Level sets and continuity of conjugate convex functions
    • R. T. Rockafellar, Level sets and continuity of conjugate convex functions. Trans. Amer. Math. Soc. 123 (1966), 46–63.
    • (1966) Trans. Amer. Math. Soc. , vol.123 , pp. 46-63
    • Rockafellar, R.T.1
  • 77
    • 84972539430 scopus 로고
    • Extension of Fenchel’s duality theorem for convex functions
    • R. T. Rockafellar, Extension of Fenchel’s duality theorem for convex functions, Duke Math. J. 33 (1966), 81–89.
    • (1966) Duke Math. J. , vol.33 , pp. 81-89
    • Rockafellar, R.T.1
  • 78
    • 0001091630 scopus 로고
    • Local boundedness of Nonlinear, Monotone Operators
    • R. T. Rockafellar, Local boundedness of Nonlinear, Monotone Operators, Michigan Math. J. 16 (1969), 397–407.
    • (1969) Michigan Math. J , vol.16 , pp. 397-407
    • Rockafellar, R.T.1
  • 79
    • 0011667369 scopus 로고
    • On the Virtual Convexity of the Domain and Range of a Nonlinear Maximal Monotone Operator
    • R. T. Rockafellar, On the Virtual Convexity of the Domain and Range of a Nonlinear Maximal Monotone Operator, Math. Ann. 185 (1970), 81–90.
    • (1970) Math. Ann. , vol.185 , pp. 81-90
    • Rockafellar, R.T.1
  • 80
    • 84966211401 scopus 로고
    • On the Maximality of Sums of Nonlinear Monotone Operators
    • R. T. Rockafellar, On the Maximality of Sums of Nonlinear Monotone Operators, Trans. Amer. Math. Soc. 149 (1970), 75–88.
    • (1970) Trans. Amer. Math. Soc. , vol.149 , pp. 75-88
    • Rockafellar, R.T.1
  • 81
    • 84972582929 scopus 로고
    • On the maximal monotonicity of subdifferential mappings
    • R. T. Rockafellar, On the maximal monotonicity of subdifferential mappings, Pac. J. Math. 33 (1970), 209-216.
    • (1970) Pac. J. Math. , vol.33 , pp. 209-216
    • Rockafellar, R.T.1
  • 82
    • 0003654177 scopus 로고
    • Monotone operators associated with saddle–functions and minimax problems
    • R. T. Rockafellar, Monotone operators associated with saddle–functions and minimax problems, Proc. Symp. Pure Math. 18 (1970), 241-250.
    • (1970) Proc. Symp. Pure Math , vol.18 , pp. 241-250
    • Rockafellar, R.T.1
  • 85
    • 0036687209 scopus 로고    scopus 로고
    • A new minimax theorem and a perturbed James’s theorem
    • M. Ruiz Galán and S. Simons, A new minimax theorem and a perturbed James’s theorem, Bull. Austral. Math. Soc. 66 (2002), 43–56.
    • (2002) Bull. Austral. Math. Soc. , vol.66 , pp. 43-56
    • Galán, M.R.1    Simons, S.2
  • 86
    • 0000147839 scopus 로고
    • On stability problems of some properties in Banach spaces, in Function spaces
    • K. Jarosz, ed., Marcel Dekker, New York
    • E. Saab and P. Saab, On stability problems of some properties in Banach spaces, in Function spaces, K. Jarosz, ed., Lecture notes in pure and applied mathematics 136 (1992), 367–394, Marcel Dekker, New York.
    • (1992) Lecture Notes in Pure and Applied Mathematics , vol.136 , pp. 367-394
    • Saab, E.1    Saab, P.2
  • 87
    • 49949123368 scopus 로고
    • Extended and sandwich versions of the Hahn–Banach Theorem
    • S. Simons, Extended and sandwich versions of the Hahn–Banach Theorem, J. Math. Anal. Appl. 21 (1968), 112–122.
    • (1968) J. Math. Anal. Appl. , vol.21 , pp. 112-122
    • Simons, S.1
  • 88
    • 0041625072 scopus 로고
    • Minimal sublinear functionals
    • S. Simons, Minimal sublinear functionals, Studia Math. 37 (1970), 37–56.
    • (1970) Studia Math , vol.37 , pp. 37-56
    • Simons, S.1
  • 90
    • 9744265189 scopus 로고    scopus 로고
    • Critères de faible compacité en termes du théorème de minimax
    • S. Simons, Critères de faible compacité en termes du théorème de minimax, Séminaire Choquet 1970/1971, no. 24, 5 pages.
    • Séminaire Choquet 1970/1971 , vol.24 , pp. 5
    • Simons, S.1
  • 91
    • 0026238781 scopus 로고
    • The least slope of a convex function and the maximal monotonicity of its subdifferential
    • S. Simons, The least slope of a convex function and the maximal monotonicity of its subdifferential, J. of Optimization Theory 71 (1991), 127–136.
    • (1991) J. of Optimization Theory , vol.71 , pp. 127-136
    • Simons, S.1
  • 92
    • 84971790885 scopus 로고
    • Subdifferentials are locally maximal monotone
    • S. Simons, Subdifferentials are locally maximal monotone, Bull. Austral. Math. Soc. 47 (1993), 465–471.
    • (1993) Bull. Austral. Math. Soc. , vol.47 , pp. 465-471
    • Simons, S.1
  • 93
    • 0042411892 scopus 로고
    • Swimming below icebergs
    • S. Simons, Swimming below icebergs, Set-Valued Anal. 2 (1994), 327–337.
    • (1994) Set-Valued Anal , vol.2 , pp. 327-337
    • Simons, S.1
  • 94
    • 38149146079 scopus 로고
    • Subtangents with controlled slope
    • S. Simons, Subtangents with controlled slope, Nonlinear Anal. 22 (1994), 1373– 1389.
    • (1994) Nonlinear Anal , vol.22 , pp. 1373-1389
    • Simons, S.1
  • 96
    • 0030123873 scopus 로고    scopus 로고
    • The range of a monotone operator
    • S. Simons, The range of a monotone operator, J. Math. Anal. Appl. 199 (1996), 176–201.
    • (1996) J. Math. Anal. Appl. , vol.199 , pp. 176-201
    • Simons, S.1
  • 97
    • 0009323251 scopus 로고    scopus 로고
    • Subdifferentials of convex functions
    • Y. Censor and S. Reich eds, American Mathematical Society, Providence, Rhode Island, Contemporary Mathematics
    • S. Simons, Subdifferentials of convex functions, in “Recent Developments in Optimization Theory and Nonlinear Analysis”, Y. Censor and S. Reich eds, American Mathematical Society, Providence, Rhode Island, Contemporary Mathematics 204 (1997), 217–246.
    • (1997) Recent Developments in Optimization Theory and Nonlinear Analysis , vol.204 , pp. 217-246
    • Simons, S.1
  • 98
    • 25444437580 scopus 로고    scopus 로고
    • Pairs of monotone operators
    • S. Simons, Pairs of monotone operators, Trans. Amer. Math. Soc. 350 (1998), 2973–2980.
    • (1998) Trans. Amer. Math. Soc , vol.350 , pp. 2973-2980
    • Simons, S.1
  • 99
    • 0012712796 scopus 로고    scopus 로고
    • Minimax and monotonicity
    • Springer–Verlag
    • S. Simons, Minimax and monotonicity, Lecture Notes in Mathematics 1693 (1998), Springer–Verlag.
    • (1998) Lecture Notes in Mathematics , vol.1693
    • Simons, S.1
  • 100
    • 0005554888 scopus 로고    scopus 로고
    • Maximal monotone multifunctions of Brøndsted–Rockafellar type
    • S. Simons, Maximal monotone multifunctions of Brøndsted–Rockafellar type, Set–Valued Anal. 7 (1999), 255–294.
    • (1999) Set–Valued Anal , vol.7 , pp. 255-294
    • Simons, S.1
  • 101
    • 0035629993 scopus 로고    scopus 로고
    • Five kinds of maximal monotonicity
    • S. Simons, Five kinds of maximal monotonicity, Set–Valued Anal. 9 (2001), 391– 409.
    • (2001) Set–Valued Anal. , vol.9 , pp. 391-409
    • Simons, S.1
  • 102
    • 0036786998 scopus 로고    scopus 로고
    • Excesses, duality gaps and weak compactness
    • S. Simons, Excesses, duality gaps and weak compactness, Proc. Amer. Math. Soc. 130 (2002), 2941–2946.
    • (2002) Proc. Amer. Math. Soc , vol.130 , pp. 2941-2946
    • Simons, S.1
  • 103
    • 0041851184 scopus 로고    scopus 로고
    • A new version of the Hahn–Banach theorem
    • S. Simons, A new version of the Hahn–Banach theorem, Arch. Math. 80 (2003), 630–646.
    • (2003) Arch. Math. , vol.80 , pp. 630-646
    • Simons, S.1
  • 105
    • 33749507839 scopus 로고    scopus 로고
    • Dualized and scaled Fitzpatrick functions
    • S. Simons, Dualized and scaled Fitzpatrick functions, Proc. Amer. Math. Soc. 134 (2006), 2983–2987.
    • (2006) Proc. Amer. Math. Soc. , vol.134 , pp. 2983-2987
    • Simons, S.1
  • 106
    • 49449107465 scopus 로고    scopus 로고
    • LC–functions and maximal monotonicity
    • S. Simons, LC–functions and maximal monotonicity, J. Nonlinear Convex Anal. 7 (2006), 123–138.
    • (2006) J. Nonlinear Convex Anal , vol.7 , pp. 123-138
    • Simons, S.1
  • 107
    • 33846487983 scopus 로고    scopus 로고
    • The Fitzpatrick function and nonreflexive spaces
    • S. Simons, The Fitzpatrick function and nonreflexive spaces, J. Convex Anal. 13 (2006), 861–881.
    • (2006) J. Convex Anal. , vol.13 , pp. 861-881
    • Simons, S.1
  • 108
    • 34250901805 scopus 로고    scopus 로고
    • Positive sets and Monotone sets
    • S. Simons, Positive sets and Monotone sets, J. Convex Anal. 14 (2007), 297–317
    • (2007) J. Convex Anal. , vol.14 , pp. 297-317
    • Simons, S.1
  • 109
    • 33745936299 scopus 로고    scopus 로고
    • Fenchel duality, Fitzpatrick functions and maximal monotonicity
    • S. Simons and C. Zălinescu, Fenchel duality, Fitzpatrick functions and maximal monotonicity, J. Nonlinear and Convex Anal. 6 (2005), 1–22.
    • (2005) J. Nonlinear and Convex Anal. , vol.6 , pp. 1-22
    • Simons, S.1    Zălinescu, C.2
  • 110
    • 0345359861 scopus 로고    scopus 로고
    • Fixed points in the family of convex representations of a maximal monotone operator
    • B. F. Svaiter, Fixed points in the family of convex representations of a maximal monotone operator, Proc. Amer. Math. Soc. 131 (2003), 3851– 3859.
    • (2003) Proc. Amer. Math. Soc. , vol.131 , pp. 3851-3859
    • Svaiter, B.F.1
  • 112
    • 0001012728 scopus 로고
    • Multifunctions with convex closed graph
    • C. Ursescu, Multifunctions with convex closed graph, Czechoslovak Math. J. 25 (1975), 438–441.
    • (1975) Czechoslovak Math. J. , vol.25 , pp. 438-441
    • Ursescu, C.1
  • 113
    • 0041627266 scopus 로고
    • Remarks on subgradients and ε-subgradients
    • A. M. E. Verona, Remarks on subgradients and ε-subgradients, Set– Valued Anal. 1 (1993), 261–272.
    • (1993) Set– Valued Anal , vol.1 , pp. 261-272
    • Verona, A.M.E.1
  • 114
    • 0043190069 scopus 로고    scopus 로고
    • Regular maximal monotone operators
    • A. M. E. Verona, Regular maximal monotone operators, Set-Valued Anal. 6 (1998), 303–312.
    • (1998) Set-Valued Anal , vol.6 , pp. 303-312
    • Verona, A.M.E.1
  • 115
    • 85174220300 scopus 로고    scopus 로고
    • Regular maximal monotone operators and the sum theorem
    • A. M. E. Verona, Regular maximal monotone operators and the sum theorem, J. Convex Anal. 7 (2000), 115–128.
    • (2000) J. Convex Anal. , vol.7 , pp. 115-128
    • Verona, A.M.E.1
  • 116
    • 34547611509 scopus 로고    scopus 로고
    • A maximality theorem for the sum of maximal monotone operators in non–reflexive Banach spaces
    • M. D. Voisei, A maximality theorem for the sum of maximal monotone operators in non–reflexive Banach spaces, Math. Sci. Res. J. 10 (2006), 36–41.
    • (2006) Math. Sci. Res. J. , vol.10 , pp. 36-41
    • Voisei, M.D.1
  • 118
    • 26444432893 scopus 로고    scopus 로고
    • The maximal monotonicity of the subdifferentials of convex functions: Simons’ problem
    • D. Zagrodny, The maximal monotonicity of the subdifferentials of convex functions: Simons’ problem, Set–Valued Anal. 4 (1996), 301–314.
    • (1996) Set–Valued Anal , vol.4 , pp. 301-314
    • Zagrodny, D.1
  • 120
    • 33745961812 scopus 로고    scopus 로고
    • A new proof of the maximal monotonicity of the sum using the Fitzpatrick function
    • Springer, New York
    • C. Zălinescu, A new proof of the maximal monotonicity of the sum using the Fitzpatrick function, in Variational analysis and applications, Nonconvex Optim. Appl. 79 1159–1172. Springer, New York, 2005.
    • (2005) Variational Analysis and Applications, Nonconvex Optim. Appl. 79 , pp. 1159-1172
    • Zălinescu, C.1
  • 121
    • 33846533684 scopus 로고    scopus 로고
    • A new convexity property for monotone operators
    • C. Zălinescu, A new convexity property for monotone operators, J. Convex Anal. 13 (2006), 883–887.
    • (2006) J. Convex Anal , vol.13 , pp. 883-887
    • Zălinescu, C.1


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