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Open AccessArticle

Generalized Integral Inequalities for Hermite–Hadamard-Type Inequalities via s-Convexity on Fractal Sets

by Ohud Almutairi 1,† and Adem Kılıçman 2,*,†
1
Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia
2
Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, Serdang 43400, Malaysia
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(11), 1065; https://doi.org/10.3390/math7111065
Received: 23 September 2019 / Revised: 31 October 2019 / Accepted: 1 November 2019 / Published: 6 November 2019
In this article, we establish new Hermite–Hadamard-type inequalities via Riemann–Liouville integrals of a function ψ taking its value in a fractal subset of R and possessing an appropriate generalized s-convexity property. It is shown that these fractal inequalities give rise to a generalized s-convexity property of ψ . We also prove certain inequalities involving Riemann–Liouville integrals of a function ψ provided that the absolute value of the first or second order derivative of ψ possesses an appropriate fractal s-convexity property. View Full-Text
Keywords: s-convex function; Hermite–Hadamard inequalities; Riemann–Liouville fractional integrals; fractal space s-convex function; Hermite–Hadamard inequalities; Riemann–Liouville fractional integrals; fractal space
MDPI and ACS Style

Almutairi, O.; Kılıçman, A. Generalized Integral Inequalities for Hermite–Hadamard-Type Inequalities via s-Convexity on Fractal Sets. Mathematics 2019, 7, 1065.

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