A VARIANTE OF KATUGAMPOLA MILNE-TYPE INEQUALITIES FOR DIFFERENTIABLE s-CONVEX FUNCTIONS

Hicham Saber, Abdelkader Moumen (), Badreddine Meftah (), Hamid Boulares (), Moheddine Imsatfia (), Rafik Guefaifia and Ibrahim Mekawy
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Hicham Saber: Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia
Abdelkader Moumen: Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia
Badreddine Meftah: Laboratory of Analysis and Control of Differential Equations “ACED†, Faculty MISM, Department of Mathematics, University of 8 Mai 1945 Guelma, P.O. Box 401, Guelma 24000, Algeria
Hamid Boulares: Laboratory of Analysis and Control of Differential Equations “ACED†, Faculty MISM, Department of Mathematics, University of 8 Mai 1945 Guelma, P.O. Box 401, Guelma 24000, Algeria
Moheddine Imsatfia: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Rafik Guefaifia: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Ibrahim Mekawy: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-18

Abstract: In this study, we focus on examining Milne’s error bounds through the use of Katugampola fractional integral operators. To attain this, we commence by presenting a novel integral identity, which will serve as the basis for proving different new Milne-type inequalities for differentiable s-convex functions, thereby generalizing certain known results in the literature. The study concludes with a few applications to special means.

Keywords: Nonlinear Equations; s-Convex Functions; Milne-type Inequalities; Power Mean Inequality Katugampola Fractional Integral Operators; Hölder’s Inequality (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401024

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