Support-type properties of generalized convex functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:365

Article

Wasowicz, Szymon

关键词: Chebyshev system;    Convexity;    Generalized convexity;    Characterization of convexity;    Support theorem;    Unique supports;    Osculatory interpolation;   

DOI  :  10.1016/j.jmaa.2009.10.070

来源: Elsevier

【 摘 要 】

Chebyshev systems induce in a natural way a concept of convexity. The functions convex in this sense behave in many aspects similarly to ordinary convex functions. In this paper support-type properties are investigated. Using osculatory interpolation. the existence of support-like functions is established for functions convex with respect to Chebyshev systems. Unique supports are determined. A characterization of the generalized convexity via support properties is presented. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free