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

Author

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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)

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.

Suggested Citation

  • Humaira Kalsoom & Bandar Almohsen, 2025. "NEW FRACTIONAL-TYPE INEQUALITIES FOR GENERALIZED n-POLYNOMIAL CONVEXITY IN INTERVAL-VALUED FUNCTIONS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(07), pages 1-18.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:07:n:s0218348x25500604
    DOI: 10.1142/S0218348X25500604
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