Preprint Article Version 1 This version is not peer-reviewed

New Generalized the Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

Version 1 : Received: 12 February 2020 / Approved: 12 February 2020 / Online: 12 February 2020 (12:38:39 CET)

How to cite: Almutairi, O.; Kılıçman, A. New Generalized the Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals. Preprints 2020, 2020020161 (doi: 10.20944/preprints202002.0161.v1). Almutairi, O.; Kılıçman, A. New Generalized the Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals. Preprints 2020, 2020020161 (doi: 10.20944/preprints202002.0161.v1).

Abstract

In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. We derive trapezoid and mid-point type inequalities connected to these generalized Hermite-Hadamard inequality.

Subject Areas

Convex function; generalized convex function; Hermite–Hadamard inequality; Katugampola fractional integral

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