FRACTAL HADAMARD–MERCER-TYPE INEQUALITIES WITH APPLICATIONS

Saad Ihsan Butt (), Saba Yousaf (), Muhammad Younas (), Hijaz Ahmad and Shao-Wen Yao
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Saad Ihsan Butt: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
Saba Yousaf: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
Muhammad Younas: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
Hijaz Ahmad: Information Technology Application and Research Center, Istanbul Ticaret University, 34445 Istanbul, Turkey3Department of Mathematics, Faculty of Humanities and Social Sciences, Istanbul Ticaret University, 34445 Istanbul, Turkey
Shao-Wen Yao: School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 02, 1-14

Abstract: Fractal analysis is a totally new area of research based on local fractional calculus. It has interesting applications in various fields such as a complex graph, computer graphics, the music industry, picture compression and many more fields. In this paper, we present new variants of Hadamard–Mercer-type inequalities on fractal sets ℠α (0 < α ≤ 1) by employing generalized convex function. We establish two new lemmas involving local fractional integrals. By using these lemmas, we obtain several results related to generalized Hadamard–Mercer-type integral inequalities for local differentiable generalized convex functions on real linear fractal space. Finally, we give applications for probability density functions and compute new generalized means.

Keywords: Jensen–Mercer Inequality; Fractal Space; Generalized Convex Function; Generalized Hermite–Hadamard Inequality; Local Fractional Derivative; Local Fractional Integral (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0218348X22400552

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