Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions
Abstract
In this study, by using an integral identity, Hölder integral inequality and modulus properties we obtain some new general inequalities of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are arithmetically harmonically (AH) convex. In the last part of the article, applications including arithmetic mean, geometric mean, harmonic mean, logarithmic mean and p-logarithmic mean, which are some special means of real numbers, are given by using arithmetic harmonically convex functions.
Keywords
Convex function, Arithmetic-harmonically convex function, Hermite-Hadamard and Bullen type inequality.
Project Number
BAP [2022/69002-03]
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