Support-type properties of generalized convex functions

被引：6

作者：

Wasowicz, Szymon ^{[1
]}

机构：

[1] Univ Bielsko Biala, Dept Math & Comp Sci, PL-43309 Bielsko Biala, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 365卷 / 01期

关键词：

Chebyshev system; Convexity; Generalized convexity; Characterization of convexity; Support theorem; Unique supports; Osculatory interpolation; HADAMARD-TYPE INEQUALITIES; HIGHER-ORDER;

D O I：

10.1016/j.jmaa.2009.10.070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：415 / 427

页数：13

共 24 条

[1] [Anonymous], 1966, PURE APPL MATH
[2] [Anonymous], 2002, RGMIA MONOGRAPHS
[3] [Anonymous], 2005, AEQUATIONES MATH
[4] Beckenbach E.F., 1937, Bull. Amer. Math. Soc, V43, P363
[5] Characterizations of convexity via Hadamard's inequality
Bessenyei, M
Páles, Z
[J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2006, 9 (01): : 53 - 62
[6] Bessenyei M, 2004, PUBL MATH DEBRECEN, V65, P223
[7] Bessenyei M, 2003, MATH INEQUAL APPL, V6, P379
[8] Bessenyei M, 2002, PUBL MATH DEBRECEN, V61, P623
[9] Bessenyei M., 2008, J. Inequal. Pure Appl. Math., V9
[10] BESSENYEI M, J MATH ANAL AP UNPUB

← 1 2 3 →