LOCAL FRACTIONAL OSTROWSKI-TYPE INEQUALITIES FOR GENERALIZED s-φ-CONVEX FUNCTION ON FRACTAL SETS

Yanrong An (), Muhammad Aamir Ali, Chenchen Xu (), Wei Liu () and Fangfang Shi ()
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Yanrong An: School of Management, Nanjing University of Posts and Telecommunications, Nanjing 210003, P. R. China
Muhammad Aamir Ali: ��School of Mathematics, Hohai University, Nanjing 210098, P. R. China
Chenchen Xu: ��School of Mathematics, Hohai University, Nanjing 210098, P. R. China
Wei Liu: ��School of Mathematics, Hohai University, Nanjing 210098, P. R. China
Fangfang Shi: ��School of Mathematics, Hohai University, Nanjing 210098, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 01, 1-12

Abstract: The main aim of this paper is to present a class of Ostrowski-type inequalities for generalized s-φ-convex functions on fractal sets, which have important applications in mathematical modeling and analysis in fields where fractal structures are prevalent, such as in signal processing, image analysis, and complex systems. For this purpose, we first define the s-φ-convex function on fractal sets and discuss some of its interesting properties. Then, we derive a generalized integral identity for nth-order locally differentiable functions, and using it, we derive some new Ostrowski-type inequalities for generalized s-φ-convex functions in a local fractal operator environment. In addition, we further illustrate the accuracy of our results with some numerical examples.

Keywords: Fractal Set; Generalized s-φ-Convex Function; Generalized Ostrowski Inequality; Local Fractional Operator (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500203

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