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Optimization of functions on certain subsets of Banach spaces. (English) Zbl 0365.49006


MSC:

49J27 Existence theories for problems in abstract spaces
46B99 Normed linear spaces and Banach spaces; Banach lattices
47H99 Nonlinear operators and their properties

References:

[1] Asplund, E.: Frechet differentiability of convex functions. Acta Math.121, 31-47 (1968) · Zbl 0162.17501 · doi:10.1007/BF02391908
[2] Asplund, E., Rockafellar, R. T.: Gradients of convex functions. Trans, AMS139, 443-467 (1969) · Zbl 0181.41901 · doi:10.1090/S0002-9947-1969-0240621-X
[3] Bishop, E., Phelps, R. R.: The support functionals of a convex set. In: Convexity. Proc. Sym. Pure math.7. Providence: AMS 1963 · Zbl 0149.08601
[4] Bourgain, J.: Strongly exposed points in weakly compact, convex sets in Banach spaces. Proc. AMS58, 197-200 (1976) · Zbl 0309.46009 · doi:10.1090/S0002-9939-1976-0415272-3
[5] Bourgain, J.: On dentability and the Bishop-Phelps property (to appear, Israel Math. J.) · Zbl 0365.46021
[6] Brøndsted, A., Rockafellar, R. T.: On the subdifferentiability of convex functions. Proc. AMS16, 605-611 (1965) · Zbl 0141.11801
[7] Diestel, J., Uhl, J. J., Jr.: Vector measures. Providence: AMS 1977 · Zbl 0369.46039
[8] Lindenstrauss, J.: On operators which attain their norm. Israel J. Math.1, 139-148 (1963) · Zbl 0127.06704 · doi:10.1007/BF02759700
[9] Rockafellar, R. T.: Convex analysis. Princeton: Princeton University Press 1970 · Zbl 0193.18401
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