MILNE-TYPE FRACTAL INTEGRAL INEQUALITIES FOR GENERALIZED m-CONVEX MAPPING

SA’UD AL-SA’DI (), Maria Bibi (), Youngsoo Seol and Muhammad Muddassar ()
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SA’UD AL-SA’DI: Department of Mathematics, Faculty of Science, The Hashemite University, P. O. Box 330127, Zarqa 13133, Jordan
Maria Bibi: Department of Basic Sciences, University of Engineering and Technology Taxila, Taxila 47050, Pakistan
Youngsoo Seol: Department of Mathematics, Dong-A University, Busan 49315, Korea
Muhammad Muddassar: Department of Basic Sciences, University of Engineering and Technology Taxila, Taxila 47050, Pakistan

FRACTALS (fractals), 2023, vol. 31, issue 05, 1-18

Abstract: In this paper, we investigate the generalized Milne-type integral inequalities via the framework of generalized m-convex mappings on fractal sets. To accomplish this, we propose a new generalized integral identity that involves differentiable generalized m-convex mappings. Based on the latest identity we drive a number of the latest fractal Milne-type integral inequalities. Also, we provide fractal Milne-type inequalities for bounded mappings. Some illustrative examples and applications to additional inequalities for the generalized special means and various error estimates for the generalized Milne-type quadrature formula are obtained to further support our results. The findings presented in this research offer important generalizations and extensions of previous work in the field.

Keywords: Milne-Type Fractal Integral Inequalities; Fractal Set; Local Fractional Derivatives; Generalized m-Convex Mappings; Local Fractional Integrals (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500810

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