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Generalized n -Polynomial p -Convexity and Related Inequalities

Author

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  • Serap Özcan

    (Department of Mathematics, Faculty of Arts and Sciences, Kırklareli University, 39100 Kırklareli, Turkey)

  • Luminiţa-Ioana Cotîrlă

    (Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania)

Abstract

In this paper, we construct a new class of convex functions, so-called generalized n -polynomial p -convex functions. We investigate their algebraic properties and provide some relationships between these functions and other types of convex functions. We establish Hermite–Hadamard (H–H) inequality for the newly defined class of functions. Additionally, we derive refinements of H–H inequality for functions whose first derivatives in absolute value at certain power are generalized n -polynomial p -convex. When p = − 1 , our definition evolves into a new definition for the class of convex functions so-called generalized n -polynomial harmonically convex functions. The results obtained in this study generalize regarding those found in the existing literature. By extending these particular types of inequalities, the objective is to unveil fresh mathematical perspectives, attributes and connections that can enhance the evolution of more resilient mathematical methodologies. This study aids in the progression of mathematical instruments across diverse scientific fields.

Suggested Citation

  • Serap Özcan & Luminiţa-Ioana Cotîrlă, 2024. "Generalized n -Polynomial p -Convexity and Related Inequalities," Mathematics, MDPI, vol. 12(7), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1042-:d:1367628
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    References listed on IDEAS

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    1. Muhammad Amer Latif, 2023. "Hermite–Hadamard-Type Inequalities for Coordinated Convex Functions Using Fuzzy Integrals," Mathematics, MDPI, vol. 11(11), pages 1-25, May.
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