Functionally closed sets and functionally convex sets in real Banach spaces

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Eshaghi Madjid; REISI DEZAKI HAMIDREZA; MOAZZEN ALIREZA

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Paper Information

Journal: INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS Year:2016 | Volume:7 | Issue:1 Page(s): 289-294

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Title

Functionally closed sets and functionally convex sets in real Banach spaces

Author(s)

Eshaghi Madjid | REISI DEZAKI HAMIDREZA | MOAZZEN ALIREZA | Issue Writer Certificate

Keywords

Convex set

Chebyshev set

Krein-Milman theorem

Abstract

Let X be a real normed space, then C( X) is functionally convex (brie y, F-convex), if T(C) R is convex for all bounded linear transformations T 2 B(X; R); and K( X) is functionally closed (brie y, F-closed), if T(K) R is closed for all bounded linear transformations T 2 B(X; R). We improve the Krein-Milman theorem on nite dimensional spaces. We partially prove the Chebyshev 60 years old open problem. Finally, we introduce the notion of functionally convex functions. The function f on X is functionally convex (brie y, F-convex) if epi f is a F-convex subset of X R. We show that every function f: (a; b) 􀀀 ! R which has no vertical asymptote is F-convex.

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APA: Copy

Eshaghi, Madjid, REISI DEZAKI, HAMIDREZA, & MOAZZEN, ALIREZA. (2016). Functionally closed sets and functionally convex sets in real Banach spaces. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 7(1), 289-294. SID. https://sid.ir/paper/340731/en

Vancouver: Copy

Eshaghi Madjid, REISI DEZAKI HAMIDREZA, MOAZZEN ALIREZA. Functionally closed sets and functionally convex sets in real Banach spaces. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS[Internet]. 2016;7(1):289-294. Available from: https://sid.ir/paper/340731/en

IEEE: Copy

Madjid Eshaghi, HAMIDREZA REISI DEZAKI, and ALIREZA MOAZZEN, “Functionally closed sets and functionally convex sets in real Banach spaces,” INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, vol. 7, no. 1, pp. 289–294, 2016, [Online]. Available: https://sid.ir/paper/340731/en

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