Extended Hermite-Hadamard $(H-H)$ and Fejer's inequalities based on $(h_1,h_2,s)$-convex functions

Document Type : Research Paper

Authors

1 Department of Mathematics and Statistics, School of Quantitative Sciences, Utara University, Malaysia, 06010 UUM Sintok, Kedah, Malaysia

2 Centre for Testing, Measurement and Appraisal, Utara University, Malaysia, 06010 UUM Sintok, Kedah, Malaysia

Abstract

In this paper, $(h_1,h_2)$-convex and $s$-convex functions are merged to form $(h_1,h_2,s)$-convex function. Inequalities of the Hermite-Hadamard (H-H) and Fejer's types will then be extended by using the $(h_1,h_2,s)$-convex function and its derivatives. Some special cases for these extended H-H and Fejer's inequalities are also explored in order to get the previously specified results. The relationship between newly constructed Hermite-Hadamard $(H-H)$ and Fejer's types of inequalities with the average (mean) values are also discussed.

Keywords