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A Study of Uniform Harmonic χ -Convex Functions with respect to Hermite-Hadamard's Inequality and Its Caputo-Fabrizio Fractional Analogue and Applications

Abstract:

In this paper, we introduce the notion of uniform harmonic χ-convex functions. We show that this class relates several other unrelated classes of uniform harmonic convex functions. We derive a new version of Hermite-Hadamard's inequality and its fractional analogue. We also derive a new fractional integral identity using Caputo-Fabrizio fractional integrals. Utilizing this integral identity as an auxiliary result, we obtain new fractional Dragomir-Agarwal type of inequalities involving differentiable uniform harmonic χ-convex functions. We discuss numerous new special cases which show that our results are quite unifying. Finally, in order to show the significance of the main results, we discuss some applications to means of positive real numbers.