**Volume 17, Issue 4, pp 465-476**

**Publication Date**: 2017-09-23

http://dx.doi.org/10.22436/jmcs.017.04.03

Muhammad Aslam Noor - Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan

Khalida Inayat Noor - Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan

Farhat Safdar - Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan

In this paper, we introduce and investigate a new class of generalized convex functions, called generalized log-convex function. We establish some new Hermite-Hadamard integral inequalities via generalized log-convex functions. Our results represent refinement and improvement of the previously known results. Several special cases are also discussed. The concepts and techniques of this paper may stimulate further research in this field.

Generalized convex functions, generalized \(\log\)-convex functions, Hermite-Hadamard type inequalities

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