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

Authors : Sevda Sezer

Pages : 88-99

Doi:10.33401/fujma.881979

View : 16 | Download : 8

Publication Date : 2021-06-01

Article Type : Research

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