Bounded approximants to monotone operators on Banach spaces
Annales de l'I.H.P. Analyse non linéaire (1992)
- Volume: 9, Issue: 5, page 573-595
- ISSN: 0294-1449
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topFitzpatrick, S., and Phelps, R. R.. "Bounded approximants to monotone operators on Banach spaces." Annales de l'I.H.P. Analyse non linéaire 9.5 (1992): 573-595. <http://eudml.org/doc/78291>.
@article{Fitzpatrick1992,
author = {Fitzpatrick, S., Phelps, R. R.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Mosco convergence; maximal monotone set-valued operator; subdifferentials; inf-convolution; approximation scheme; Moreau-Yosida approximation method; non-reflexive Banach spaces},
language = {eng},
number = {5},
pages = {573-595},
publisher = {Gauthier-Villars},
title = {Bounded approximants to monotone operators on Banach spaces},
url = {http://eudml.org/doc/78291},
volume = {9},
year = {1992},
}
TY - JOUR
AU - Fitzpatrick, S.
AU - Phelps, R. R.
TI - Bounded approximants to monotone operators on Banach spaces
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1992
PB - Gauthier-Villars
VL - 9
IS - 5
SP - 573
EP - 595
LA - eng
KW - Mosco convergence; maximal monotone set-valued operator; subdifferentials; inf-convolution; approximation scheme; Moreau-Yosida approximation method; non-reflexive Banach spaces
UR - http://eudml.org/doc/78291
ER -
References
top- [As] E. Asplund, Fréchet Differentiability of Convex Functions, Acta Math., Vol. 121, 1968, pp. 31-47. Zbl0162.17501MR231199
- [At] H. Attouch, Variational Convergence for Functions and Operators, Pitman, 1984. Zbl0561.49012MR773850
- [A-N-T] H. Attouch, J.L. Ndoutoume and M. Thera, Epigraphical Convergence of Functions and Convergence of their Derivatives in Banach Spaces, Sem. d'Analyse Convexe, Montpellier, 1990, Exposé No. 9. Zbl0764.46042MR1114679
- [Bai] R. Baire, Leçons sur les fonctions discontinues, Gauthier-Villars, Paris, 1905. Zbl0897.01040JFM36.0438.01
- [B-F] J. Borwein and S.P. Fitzpatrick, Local Boundedness of Monotone Operators Under Minimal Hypotheses, Bull. Australian Math. Soc., Vol. 39, 1989, pp. 439- 441. Zbl0694.47040MR995141
- [B-C-P] H. Brezis, M. Crandall and A. Pazy, Perturbations of Nonlinear Maximal Monotone Sets, Comm. Pure Appl. Math., Vol. 23, 1970, pp. 123-144. Zbl0182.47501MR257805
- [Da] M.M. Day, Normed Linear Spaces, 3rd Ed., Egeb. der Math. u. ihrer Grenzgeb., Band 21, Springer-Verlag, 1973. Zbl0268.46013MR344849
- [D-F] H. Debrunner and P. Flop, Ein Erweiterungssatz für monotone Mengen, Arch. Math., Vol. 15, 1964, pp. 445-447. Zbl0129.09203MR170189
- [De] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985. Zbl0559.47040MR787404
- [Go1] J.-P. Gossez, Opérateurs monotones non linéaires dans les espaces de Banach non réflexifs, J. Math. Anal. Appl., Vol. 34, 1971, pp. 371-395. Zbl0228.47040MR313890
- [Go2] J.-P. Gossez, On the Range of a Coercive Maximal Monotone Operator in a Nonreflexive Banach Space, Proc. Amer. Math. Soc., Vol. 35, 1972, pp. 88-92. Zbl0251.47050MR298492
- [Go3] J.-P. Gossez, On a Convexity Property of the Range of a Maximal Monotone Operator, Proc. Amer. Math. Soc., Vol. 55, 1976, pp. 359-360. Zbl0331.47029MR397485
- [Hau] F. Hausdorff, Über halbstetige Funcktionen und deren Verallgemeinerung, Math. Zeit., Vol. 5, 1919, pp. 292-309. Zbl47.0240.01MR1544388JFM47.0240.01
- [H-U1] J.-B. Hiriart-Urruty, Lipschitz r-Continuity of the Approximate Subdifferential of a Convex Function, Math. Scand., Vol. 47, 1980, pp. 123-134. Zbl0426.26005MR600082
- [H-U2] J.-B. Hiriart-Urruty, Extension of Lipschitz Functions, J. Math. Anal. Appl., Vol. 77, 1980, pp. 539-554. Zbl0455.26006MR593233
- [K-N] H. König and M. Neumann, Mathematische Wirtschaftstheorie (mit einer Einführung in die konvexe Analysis), Mathematical Systems in Economics, vol. 100, 1986, Hain Verlag, Königstein. Zbl0591.90001MR842432
- [La] P.-J. Laurent, Approximation et Optimisation, Hermann, Paris, 1972. Zbl0238.90058MR467080
- [Lu] F.J. Luque, Convolutions of Maximal Monotone Mappings (preprint).
- [McS] E.J. Mcshane, Extension of Range of Functions, Bull. Amer. Math. Soc., Vol. 40, 1934, pp. 837-842. Zbl0010.34606
- [No1] D. Noll, Generic Gateaux Differentiability of Convex Functions on Small Sets, J. Math. Analysis and Applications, Vol. 147, 1990, pp. 531-544. Zbl0715.46019MR1050225
- [No2] D. Noll, Generic Fréchet Differentiability of Convex Functions on Small Sets, Arch. Math., Vol. 54, 1990, pp. 487-492. Zbl0666.46049MR1049204
- [P-S] D. Pascali and S. Sburlan, Nonlinear Mappings of Monotone Type, Sijthoff and Noordhoff, 1978. Zbl0423.47021MR531036
- [Pa] G.B. Passty, The Parallel Sum of Nonlinear Monotone Operators, Nonlin. Analysis. Theory, Methods and Appl., Vol. 10, 1986, pp. 215-227. Zbl0628.47033MR834503
- [Ph] R.R. Phelps, Convex Functions, Monotone Operators and Differentiability, Lecture Notes in Math., No. 1364, Springer-Verlag, 1989. Zbl0658.46035MR984602
- [Ro1] R.T. Rockafellar, Local Boundedness of Nonlinear, Monotone Operators, Mich. Math. J., Vol. 16, 1969, pp. 397-407. Zbl0175.45002MR253014
- [Ro2] R.T. Rockafellar, Sums of Nonlinear Monotone Operators, Trans. Amer. Math. Soc., Vol. 149, 1970, pp. 75-88. Zbl0222.47017MR282272
- [Ro3] R.T. Rockafellar, On the Virtual Convexity of the Domain and Range of a Nonlinear Maximal Monotone Operator, Math. Ann., Vol. 185, 1970, pp. 81-90. Zbl0181.42202MR259697
- [Ro4] R.T. Rockafellar, Characterization of the Subdifferentials of Convex Functions, Pacific J. Math., Vol. 17, 1966, pp. 497-510. Zbl0145.15901MR193549
- [Ro5] R.T. Rockafellar, On the Maximal Monotonicity of Subdifferential Mappings, Pacific J. Math., Vol. 33, 1970, pp. 209-216. Zbl0199.47101MR262827
- [Si] S. Simons, The Least Slope of a Convex Function and the Maximal Monotonicity of its Subdifferential, J. Optimization Theory and Applications (to appear). Zbl0795.49016
- [To] R.M. Torrejon, Parturbation of Nonlinear Operators and their Parallel Sum, Nonlin. Analysis. Theory, Methods and Appl., Vol. 10, 1986, pp. 483-490. Zbl0607.47068MR839360
- [Tu] A.W. Tucker, Dual Systems of Homogeneous Linear Equations, Linear Inequali- ties and Related Systems, H. W. KUHN and A. W. TUCKER Eds., Annals of Math. Studies, Vol. 38, 1956, pp. 3-18. Zbl0072.37503
- [Wh] H. Whitney, Analytic Extensions of Differentiable Functions Defined on Closed Sets, Trans. Amer. Math. Soc., Vol. 36, 1934, pp. 63-89. Zbl0008.24902MR1501735JFM60.0217.01
- [Ze] E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. II/A, Linear Monotone Operators, Vol. II/B, Nonlinear Monotone Operators, Springer-Verlag, 1985.
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