A support theorem for generalized convexity and its applications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:458

Article

Olbrys, Andrzej¹ 

[1] Univ Silesia, Inst Math, Ul Bankowa 14, PL-40007 Katowice, Poland

关键词: Convexity;    t-Convexity;    Midpoint-convexity;    Support theorem;   

DOI  :  10.1016/j.jmaa.2017.09.038

来源: Elsevier

【 摘 要 】

In the present paper we introduce a notion of (omega, t) convexity as a natural generalization of the notion of usual t-convexity, t-strongly convexity, approximate t-convexity, delta t-convexity and many other. The main result of this paper establishes the necessary and sufficient conditions under which an (omega, t)-convex map can be supported at a given point by an (omega, t)-affine support function. Several applications of this support theorem are presented. For instance, new characterizations of inner product spaces among normed spaces involving the notion of (omega, t)-convexity are given. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free