Hermite–Hadamard type inequalities for m-convex and $( \alpha , m)$-convex functions

Abstract

Abstract In this paper, some new inequalities of the Hermite–Hadamard type for the classes of functions whose derivatives’ absolute values are m -convex and $( \alpha , m) $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:math> -convex are obtained. The results obtained in this work extend and improve the corresponding ones in the literature. Some applications to special means of real numbers are also given.

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