NEW FRACTIONAL-TYPE INEQUALITIES FOR GENERALIZED n-POLYNOMIAL CONVEXITY IN INTERVAL-VALUED FUNCTIONS

Humaira Kalsoom () and Bandar Almohsen
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Humaira Kalsoom: College of Science, Nanjing Forestry University, Nanjing, Jiangsu 210037, P. R. China
Bandar Almohsen: Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 07, 1-18

Abstract: In this paper, we introduce and investigate a new class of functions known as generalized n-polynomial interval-valued convex functions. Our study focuses on exploring fractional calculus-based Hermite–Hadamard ð ’¦-fractional integral inequalities, Hermite–Hadamard–FejeÌ r-type ð ’¦-fractional integral inequalities, and various product inequalities. These results extend the classical Hermite–Hadamard integral inequalities by incorporating fractional calculus. Additionally, we provide numerical examples and graphical analyses to validate and clarify our theoretical findings. This work offers insights into the dynamic interplay between fractional calculus, polynomial convexity, and fractal geometry within interval-valued functions, contributing to both theoretical understanding and potential future advancements in this area of mathematical research.

Keywords: Hermite–Hadamard’s Inequality; Hermite–Hadamard–FejeÌ r-type; n-Polynomial Convex Function; ð ’¦-Fractional Integral Operator; Interval-Valued Function (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:33:y:2025:i:07:n:s0218348x25500604

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DOI: 10.1142/S0218348X25500604

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