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Research Article | Open Access

Fractional integral estimations pertaining to generalized γ -convex functions involving Raina's function and applications

Bandar Bin-Mohsin1, Muhammad Uzair Awan2( ), Muhammad Zakria Javed2, Artion Kashuri3, Muhammad Aslam Noor4
Department of Mathematics College of Science King Saud University, Riyadh, Saudi Arabia
Department of Mathematics, Government College University, Faisalabad, Pakistan
Department of Mathematics, Faculty of Technical and Natural Sciences, University "Ismail Qemali", 9400 Vlora, Albania
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
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Abstract

In this paper, we derive a new fractional integral identity and using this identity as an auxiliary result, some new trapezium like inequalities essentially using the class of generalized γ -convex functions are established. In order to show the efficiency of the obtained results, we discuss and present some special cases and applications.

Keywords

generalized γ-convexityJensen's integral inequalitypower mean integral inequalityfractional integralspecial meansbounded functionserror estimations
CLC number: 26D07, 26D10, 26D15, 26A33, 26A51, 60E15

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AIMS Mathematics
Volume 7 Issue 8,
August 2022
Pages 13633-13663
DOI: 10.3934/math.2022752

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Bin-Mohsin B, Awan MU, Javed MZ, et al. Fractional integral estimations pertaining to generalized γ -convex functions involving Raina's function and applications. AIMS Mathematics, 2022, 7(8): 13633-13663. https://doi.org/10.3934/math.2022752

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Received: 30 March 2022
Revised: 11 May 2022
Accepted: 17 May 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)