Yet more on the differentiability of convex functions
HTML articles powered by AMS MathViewer
- by John Rainwater PDF
- Proc. Amer. Math. Soc. 103 (1988), 773-778 Request permission
Abstract:
Generic differentiability theorems are obtained for convex functions which are defined and locally Lipschitzian on the convex subset $N(C)$ of nonsupport points of a closed convex subset $C$ of a Banach space $E$, which is assumed to be either an Asplund space (for Fréchet differentiability) or to be weakly compactly generated (for Gateaux differentiability).References
- Edgar Asplund, Fréchet differentiability of convex functions, Acta Math. 121 (1968), 31–47. MR 231199, DOI 10.1007/BF02391908
- Jens Peter Reus Christensen, Theorems of Namioka and R. E. Johnson type for upper semicontinuous and compact valued set-valued mappings, Proc. Amer. Math. Soc. 86 (1982), no. 4, 649–655. MR 674099, DOI 10.1090/S0002-9939-1982-0674099-0
- Joseph Diestel, Geometry of Banach spaces—selected topics, Lecture Notes in Mathematics, Vol. 485, Springer-Verlag, Berlin-New York, 1975. MR 0461094 John Giles, Convex analysis with application to differentiation of convex functions, Research Notes in Math., no. 58, Pitman, Boston, Mass., 1982.
- Richard B. Holmes, Geometric functional analysis and its applications, Graduate Texts in Mathematics, No. 24, Springer-Verlag, New York-Heidelberg, 1975. MR 0410335
- P. S. Kenderov, Monotone operators in Asplund spaces, C. R. Acad. Bulgare Sci. 30 (1977), no. 7, 963–964. MR 463981
- I. Namioka, Separate continuity and joint continuity, Pacific J. Math. 51 (1974), 515–531. MR 370466
- I. Namioka and R. R. Phelps, Banach spaces which are Asplund spaces, Duke Math. J. 42 (1975), no. 4, 735–750. MR 390721
- R. R. Phelps, Some topological properties of support points of convex sets, Israel J. Math. 13 (1972), 327–336 (1973). MR 328558, DOI 10.1007/BF02762808
- Charles Stegall, A class of topological spaces and differentiation of functions on Banach spaces, Proceedings of the conferences on vector measures and integral representations of operators, and on functional analysis/Banach space geometry (Essen, 1982) Vorlesungen Fachbereich Math. Univ. Essen, vol. 10, Univ. Essen, Essen, 1983, pp. 63–77. MR 730947
- C. Stegall, More Gâteaux differentiability spaces, Banach spaces (Columbia, Mo., 1984) Lecture Notes in Math., vol. 1166, Springer, Berlin, 1985, pp. 186–199. MR 827772, DOI 10.1007/BFb0074706
- Maria Elena Verona, More on the differentiability of convex functions, Proc. Amer. Math. Soc. 103 (1988), no. 1, 137–140. MR 938657, DOI 10.1090/S0002-9939-1988-0938657-3
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 773-778
- MSC: Primary 46G05; Secondary 26B05, 46B22, 58C06, 90C48
- DOI: https://doi.org/10.1090/S0002-9939-1988-0947656-7
- MathSciNet review: 947656