Hermite-Hadamard Type Inequalities for the Functions Whose Absolute Values of First Derivatives are $p$-Convex

Year 2021, Volume: 4 Issue: 2, 88 - 99, 01.06.2021

Sevda Sezer

https://doi.org/10.33401/fujma.881979

Cited By: 2

Abstract

In this paper, we extend some estimates of a Hermite-Hadamard type inequality for functions whose absolute values of the first derivatives are $p$-convex. By means of the obtained inequalities, some bound functions involving beta functions and hypergeometric functions are derived as applications. Also, we suggest an upper bound for error in numerical integration of $p$-convex functions via composite trapezoid rule.

Keywords

Hermite-Hadamard inequality, $p$-convex function, Convexity

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