Korovkin type theorems and approximate Hermite-Hadamard inequalities

Judit Makó, Zsolt Páles

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1111-1142
Number of pages32
JournalJournal of Approximation Theory
Volume164
Issue number8
DOIs
Publication statusPublished - Jul 2 2012

Keywords

  • Approximate convexity
  • Convexity
  • Korovkin type theorem
  • Lower and upper Hermite-Hadamard inequalities

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics(all)
  • Applied Mathematics

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