Integral Inequalities for s-Convexity via Generalized Fractional Integrals on Fractal Sets

Ohud Almutairi,Adem Kılıçman

doi:10.3390/math8010053

Ohud Almutairi, Adem Kılıçman

Open Access

https://doi.org/10.3390/math8010053

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Abstract

In this study, we establish new integral inequalities of the Hermite–Hadamard type for s-convexity via the Katugampola fractional integral. This generalizes the Hadamard fractional integrals and Riemann–Liouville into a single form. We show that the new integral inequalities of Hermite–Hadamard type can be obtained via the Riemann–Liouville fractional integral. Finally, we give some applications to special means.

Highlights

Fractional calculus, whose applications can be found in many disciplines including economics, life and physical sciences, as well as engineering, can be considered as one of the modern branches of mathematics [1,2,3,4]
Many problems of interests from these fields can be analyzed through fractional integrals, which can be regarded as an interesting sub-discipline of fractional calculus
Many important generalizations of Hermite–Hadamard inequality were studied [11,12,13,14,15,16,17], some of which were formulated via generalized s-convexity, which is defined as follows

Summary

Introduction

Fractional calculus, whose applications can be found in many disciplines including economics, life and physical sciences, as well as engineering, can be considered as one of the modern branches of mathematics [1,2,3,4]. The fractional integrals were extended to include the Hermite–Hadamard inequality, which is classically given as follows. The function h : [w, z] ⊂ R+ → Rα is said to be generalized s-convex on fractal sets Other important extensions of Equation (1) include the work of Mehran and Anwar [20], who studied the Hermite–Hadamard-type inequalities for s-convex functions involving generalized fractional integrals.

Results

Conclusion