Simpson’s Rule and Hermite–Hadamard Inequality for Non-Convex Functions

In this article we give a variant of the Hermite–Hadamard integral inequality for twice differentiable functions. It represents an improvement of this inequality in the case of convex/concave functions. Sharp two-sided inequalities for Simpson’s rule are also proven along with several extensions....

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Bibliographic Details
Published inMathematics (Basel) Vol. 8; no. 8; p. 1248
Main Authors Simić, Slavko, Bin-Mohsin, Bandar
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2020
Subjects
Convex analysis
convex functions
hermite-hadamard integral inequality
Inequality
Mathematics
Remakes & sequels
Theorems
twice differentiable functions
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Summary:In this article we give a variant of the Hermite–Hadamard integral inequality for twice differentiable functions. It represents an improvement of this inequality in the case of convex/concave functions. Sharp two-sided inequalities for Simpson’s rule are also proven along with several extensions.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8081248