Generalization of Hermite–Hadamard type inequalities for n-times differentiable functions through preinvexity

Muhammad Amer Latif; Sever Silvestru Dragomir

doi:10.1515/gmj-2015-0053

Published by De Gruyter January 7, 2016

Generalization of Hermite–Hadamard type inequalities for n-times differentiable functions through preinvexity

Muhammad Amer Latif and Sever Silvestru Dragomir

From the journal Georgian Mathematical Journal

https://doi.org/10.1515/gmj-2015-0053

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Abstract

In this paper, we establish a new integral identity for n-times differentiable functions defined on an invex subset of ℝ. Hermite–Hadamard type integral inequalities for n-times differentiable preinvex functions are then established by using this identity and Hölder's inequality.

Keywords: Hermite–Hadamard's inequality; invex set; preinvex function; Hölder's integral inequality

MSC: 26D15; 26A51; 26B12; 41A55

Received: 2014-3-3

Revised: 2014-4-29

Accepted: 2014-6-9

Published Online: 2016-1-7

Published in Print: 2016-3-1

Generalization of Hermite–Hadamard type inequalities for n-times differentiable functions through preinvexity

Abstract

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