(alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type

Year 2019, Volume: 68 Issue: 2, 2128 - 2142, 01.08.2019

Huriye Kadakal

https://doi.org/10.31801/cfsuasmas.511184

Cited By: 7

Abstract

In this paper, we introduce a new class of extended (alpha;m1;m2)-convex functions. Some algebraic properties of these class functions have been investigated. Some new Hermite-Hadamard type inequalities are derived. Results represent signicant refinement and improvement of the previous results. Also, the author establish a new integral identity and, by this identity, Hölder's and power mean inequality, discover some new Hermite-Hadamard type inequalities for functions whose first derivatives are (alpha;m1;m2)-convex. Our results are new and coincide with the previous results in special cases.

Keywords

Convex function, m-Convex function, (alpha;m)-Convex function, (alpha;m1;m2)-Convex function, Hermite-Hadamard type inequality

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