On uniform differentiability

• Autorzy: Rolewicz S.
• Języki publikacji: EN

Abstrakty

EN

We introduce the notion of uniform Frechet differentiability of mappings between Banach spaces, and we give some sufficient conditions for this property to hold.

Słowa kluczowe

EN

uniformly Frechet differentiable; uniformly approximately convex; subgradient; subdifferential

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2008
• Tom: Vol. 56, no 3-4
• Strony: 231--237
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Rolewicz S.

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland,

Bibliografia

• E. Asplund (1966), Farthest points in reflexive locally uniformly rotund Banach spaces, Israel J. Math. 4, 213-216.
• E. Asplund (1968), Fréchet differentiability of convex functions, Acta Math. 121, 31-47.
• A. D. Ioffe (1984), Approximate subdifferentials and applications I, Trans. Amer. Math. Soc. 281, 389-416.
• A. D. Ioffe (1986), Approximate subdifferentials and applications II, Mathematika 33, 111-128.
• A. D. Ioffe (1989), Approximate subdifferentials and applications III, ibid. 36, 1-38.
• A. D. Ioffe (1990), Proximal analysis and approximate subdifferentials, J. London Math. Soc. 41, 175-192.
• A. D. Ioffe (2000), Metric regularity and subdifferential calculus, Uspekhi Mat. Nauk 55, no. 3, 104-162 (in Russian).
• D. T. Luc, H. V. Ngai and M. Thera (1999), On ε-monotonicity and ε-convexity, in: Calculus of Variations and Differential Equations, A. Ioffe et al. (eds.), Chapman & Hall/CRC, Res. Notes Math. 410, Chapman and Hall, 82-100.
• D. T. Luc, H. V. Ngai and M. Thera (2000), Approximate convex functions, J. Nonlinear Convex Anal. 1, 155-176.
• B. S. Mordukhovich (1980), Metric approximations and necessary optimality conditions for general classes of nonsmooth extremal problems, Soviet Math. Dokl. 22, 526-530.
• B. S. Mordukhovich (1988), Approximation Methods in Problems of Optimization and Control, Nauka, Moscow (in Russian).
• S. Rolewicz (1979a), On paraconvex multifunctions, in: Oper. Research Verfahren 31, 540-546.
• S. Rolewicz (1979b), On γ-paraconvex multifunctions, Math. Japonica 24, 293-300.
• S. Rolewicz (2000), On α(ּ)-paraconvex and strongly α(ּ)-paraconvex functions, Control Cybernet. 29, 367-377.
• S. Rolewicz (2001a), On equivalence of Clarke, Dini, α(ּ)-subgradients and local α(ּ)-subgradients for strongly α(ּ)-paraconvex functions, Optimization 50, 353-360.
• S. Rolewicz (2001b), On uniformly approximate convex and strongly α(ּ)-paraconvex functions, Control Cybernet. 30, 323-330.
• S. Rolewicz (2002), α(ּ)-monotone multifunctions and differentiability of strongly α(ּ)-paraconvex functions, ibid. 31, 601-619.
• S. Rolewicz (2005), On differentiability of strongly α(ּ)-paraconvex functions in non-separable Asplund spaces, Studia Math. 167, 235-244.
• R. Rudnicki (1986), Asymptotic properties of the iterates of positive operators on C(X), Bull. Polish Acad. Sci. Math. 34, 181-187.