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

[11] Bessenyei M., 2004, Acta Sci. Math. (Szeged), V70, P13
[12] BESSENYEI M, P ROY SOC ED A UNPUB
[13] de Boor C., 2005, SURV APPROX THEORY, V1, P46
[14] GER R., 1994, WORLD SCI PUBL CO WS, V3, P255
[15] GREEN JW, 1953, P AM MATH SOC, V4, P391
[16] Hardy Godfrey Harold, 1952, Inequalities, V2nd
[17] HOPF E, 1926, THESIS F WILHELMS U
[18] Jordan C., 1965, Calculus of finite differences, V33
[19] KUCZMA M, 1985, PR NAUK UNIW SI KATO, V489
[20] Extending n-convex functions
Pinkus, A
Wulbert, D
[J]. STUDIA MATHEMATICA, 2005, 171 (02) : 125 - 152

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