no. 4
Uniformly convex and uniformly smooth convex functions
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 4 (1995) no. 4, pp. 705-730. 
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     title = {Uniformly convex and uniformly smooth convex functions},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {705--730},
     publisher = {Universit\'e Paul Sabatier},
     address = {Toulouse},
     volume = {Ser. 6, 4},
     number = {4},
     year = {1995},
     mrnumber = {1623472},
     zbl = {0870.49010},
     language = {en},
     url = {http://www.numdam.org/item/AFST_1995_6_4_4_705_0/}
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Azé, Dominique; Penot, Jean-Paul. Uniformly convex and uniformly smooth convex functions. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 4 (1995) no. 4, pp. 705-730. http://www.numdam.org/item/AFST_1995_6_4_4_705_0/

[1] Asplund (E.) .- Fréchet Differentiability of convex functions, Acta Matematica 121 (1967), pp. 31-47. | MR | Zbl

[2] Asplund (E.) .- Positivity of duality mappings, Bull. Am. Math. Soc. 73 (1967), pp. 200-203. | MR | Zbl

[3] Asplund (E.) and Rockafellar (R.T.) .- Gradients of convex functions, Trans. Am. Math. Soc. 139 (1969), pp. 443-467. | MR | Zbl

[4] Attouch (H.) and Wets (R.J.-B.) .- A quantitative approach via epigraphic distances to stability of strong local minimizers, Technical report No 87-01, Univ. of Perpignan (1987).

[5] Aubin (J.-P.) and Ekeland (I.) .- Nonlinear applied analysis, J. Wiley, New York (1984). | MR | Zbl

[6] Auslender (A.) .- Optimisation - Méthodes numériques, Masson, Paris (1976). | MR | Zbl

[7] Beauzamy (B.) .- Introduction to Banach spaces and their geometry, Mathematical Studies 68, North-Holland, Amsterdam (1982). | MR | Zbl

[8] Bishop (E.) and Phelps (R.R.) .- The support functionals of a convex set, In Convexity edited by P. Klee, Proc. Symp. Pure Math. 7, Am. Math. Soc. Providence (1963), pp. 27-35. | MR | Zbl

[9] Bröndsted (A.) and Rockafellar (R.T.) .- On the subdifferentiability of convex functions, Proc. Am. Math. Soc. 16 (1965), pp. 605-611. | MR | Zbl

[10] Browder (F.E.) .- Problèmes non linéaires, Presses de l'Université de Montréal 15 (1966). | Zbl

[11] Bynum (J.C.) .- Characterizations of uniform convexity, Pac. J. Math. 38, No 3 (1971), pp. 577-581. | MR | Zbl

[12] Ciarlet (P.G.) .- Introduction à l'analyse numérique matricielle et à l'optimisation, Masson, Paris (1982). | MR | Zbl

[13] Cioranescu (I.) .- Duality mappings in the nonlinear functional analysis, Ed. Acad. R.S.R., Bucharest (1974) (in Romanian). | MR

[14] Diestel (J.) .- Geometry of Banach spaces, selected topics, Lecture Notes in Mathematics 485, Springer, Berlin (1975). | MR | Zbl

[15] Donchev (A.L.) .- Perturbations, approximations and sensitivity analysis of optimal control systems, Springer Lecture Notes in Control 52 (1984). | MR | Zbl

[16] Dunn (J.C.) .- Convexity, monotonicity and gradient processes in Hilbert spaces, J. Math. Anal. Appl. 53 (1976), pp. 145-158. | MR | Zbl

[17] Ekeland (I.) .- Two results in convex analysis, in "Optimization and related fields", Ed. by R. Conti, E. de Giorgi and F. Giannessi, Lecture Notes in Mathematics 1190, Springer Berlin (1986). | MR | Zbl

[18] Figiel (T.) .- On the moduli of convexity and smoothness, Stud. Math. 56 (1976), pp. 121-155. | MR | Zbl

[19] Jeyakumar (V.) . - On subgradient duality with strong and weak convex functions, J. Austr. Math. Soc. 40, Ser. A (1986), 143-152. | MR | Zbl

[20] Jeyakumar (V.) . - p-convexity and second order duality, Util. Math. 29 (1986), pp. 71-85. | MR | Zbl

[21] Karmanov (V.) .- Programmation Mathématique, French translation, Mir, Moscow (1975). | Zbl

[22] Levitin (E.) and Poljak (B.), .- Minimization methods in the presence of constraints, Z. Vycisl. Mat. i. Fiz. 6, No 5 (1966), pp. 787-823. | MR | Zbl

[23] Levitin (E.) and Poljak (B.) .- Convergence of minimizing sequences in conditional extremum problems, Sov. Math. Dokl. 7 (1967), pp. 764-767. | MR | Zbl

[24] Lucchetti (R.) and Patrone (F.) .- Hadamard and Tyhonov well-posedness of a certain class of convex functions, J. Math. Anal. Appl. 88 (1982), pp. 204-215. | MR | Zbl

[25] Lyubich (Y.) and Maistrovski (G.) .- The general theory of relaxation processes for convex functionals, Russ. Math. Surv. 25 (1970), pp. 57-117. | Zbl

[26] Milman (V.D.) .- A certain transformation of convex functions and a duality of the β and δ characteristics of a β space, Dokl. Akad. Nauk. SSSR 187 (1969), pp. 33-45. | MR | Zbl

[27] Psenitchny (B.) and Daniline (Y.) .- Méthodes numériques dans les problèmes d'extremum, French translation, Mir, Moskow (1975).

[28] Penot (J.-P.) .- Metric regularity, openness and Lipschitzian behaviour of multifunctions, Nonlinear Anal. Theory Methods Appl. 13, No 6 (1989), pp. 629-643. | MR | Zbl

[29] Penot (J.-P.) and Volle (V.) .- Inversion of real valued functions and applications, Z.O.R. Methods and Models of Operations Research 34 (1990), pp. 117-141. | MR | Zbl

[30] Penot (J.-P.) and Volle (M.) .- On strongly convex and paraconvex dualities, in "Generalized Convexity and Fractional Programming with Economics Applications", Proc. Pisa. Italy (1988), A. Cambini et al. Eds. Lecture Notes in Economics and Mathematical Systems 345, Springer Verlag Berlin (1990), pp. 198-218. | MR | Zbl

[31] Poljak (B.) . - Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Sov. Math. Dokl. 7 (1967), pp. 72-75. | MR | Zbl

[32] Prüss (J.) . - A Characterization of uniform convexity and application to accretive operators, Hiroshima Math. J. 11 (1981), pp. 229-234. | MR | Zbl

[33] Roberts (A.W.) and Varberg (D.) .- Convex functions, Academic Press, New York (1973). | MR | Zbl

[34] Rockafellar (R.T.) .- Monotone operators and the proximal point algorithm, SIAM J. Control Opt. 14 (1976), pp. 877-898. | MR | Zbl

[35] Šmulyan (V.L.) .- Sur la dérivabilité de la norme dans l'espace de Banach, Dokl. Acad. Naukl. SSSR, 27 (1940), pp. 643-648. | MR | Zbl

[36] Vial (J.P.) .- Strong convexity of sets and functions, J. Math. Econ. 9 (1982) pp. 187-205. | MR | Zbl

[37] Vial (J.-P.) .- Strong and weak convexity of sets and functions, Math. Oper. Res. 8 (1983), pp. 231-259. | MR | Zbl

[38] Vladimirov (A.A.), Nesterov (Yu E.) and Chekanov (Yu N.) .- On uniformly convex functionals, Vest. Mosk. Univ. 3, Ser. XV (1978), pp. 12-23. | MR | Zbl

[39] Vladimirov (A.A.), Nesterov (Yu E.) and Chekanov (Yu N.) .- On uniformly quasi-convex functionals, Vest. Mosk. Univ. 4, Ser. XV (1978), pp. 18-27. | MR | Zbl

[40] Volle (M.) Personal communication.

[41] Zalinescu (C.) .- On uniformly convex functions, J. Math. Anal. Appl. 95 (1983), pp. 344-374. | MR | Zbl

[42] Zolezzi (T.) .- On equiwellset minimum problems, Appl. Math. Optimization 4 (1978), pp. 209-223. | MR | Zbl