Korovkin type theorems and approximate Hermite-Hadamard inequalities

JOURNAL OF APPROXIMATION THEORY

卷:164

Article

Mako, Judit¹  Pales, Zsolt¹ 

[1] Univ Debrecen, Inst Math, H-4010 Debrecen, Hungary

关键词: Convexity;    Approximate convexity;    Lower and upper Hermite-Hadamard inequalities;    Korovkin type theorem;   

DOI  :  10.1016/j.jat.2012.05.010

来源: Elsevier

【 摘 要 】

The main results of this paper offer sufficient conditions in order that an approximate lower Hermite-Hadamard type inequality implies an approximate convexity property. The failure of such an implication with constant error term shows that functional error terms should be considered for the inequalities and convexity properties in question. The key for the proof of the main result is a Korovkin type theorem which enables us to deduce the approximate convexity property from the approximate lower Hermite-Hadamard type inequality via an iteration process. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free