Advancements in Harmonic Convexity and Its Role in Modern Mathematical Analysis

Sabila Ali, Muhammad Samraiz, Saima Naheed and Miguel Vivas-Cortez

Journal of Mathematics, 2025, vol. 2025, 1-19

Abstract: Convex functions play an integral part in artificial intelligence by providing mathematical guarantees that make optimization more efficient and reliable. In this manuscript, we originate and analyze a novel category of convexity, namely, harmonically trigonometric p-convex functions, and explore their properties. We provide examples of this new class of convex functions. By leveraging the new convexity, refinements of Hermite–Hadamard-type and Fejér–Hermite–Hadamard-type inequalities are formulated. The derivation of these inequalities involves the utilization of Hölder’s inequality, Hölder–İşcan inequality, the power-mean integral inequality, and certain generalizations associated with these mathematical principles. The validity of the established results is confirmed through visual representation. A comparative analysis is provided to clarify that inequality derived through the power-mean inequality is more refined than other inequalities. Additionally, we discuss the applications of these findings to some special means.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8847839

DOI: 10.1155/jom/8847839

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