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Some weighted integral inequalities for differentiable h-preinvex functions

Muhammad Amer Latif, Sever Silvestru Dragomir and Ebrahim Momoniat

Abstract

In this paper, by using a weighted identity for functions defined on an open invex subset of the set of real numbers, by using the Hölder integral inequality and by using the notion of h-preinvexity, we present weighted integral inequalities of Hermite–Hadamard-type for functions whose derivatives in absolute value raised to certain powers are h-preinvex functions. Some new Hermite–Hadamard-type integral inequalities are obtained when h is super-additive. Inequalities of Hermite–Hadamard-type for s-preinvex functions are given as well as a special case of our results.

MSC 2010: 26D15; 26D20; 26D07

Acknowledgements

The authors thank the anonymous referee for his/her very useful comments which helped us to improve the final version of the manuscript.

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Received: 2014-09-26
Accepted: 2014-11-13
Published Online: 2017-01-19
Published in Print: 2018-09-01

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