Hermite–Hadamard-type inequalities for multiplicative harmonic $s$-convex functions

Serap Özcan; Ayça Uruṣ; Saad Ihsan Butt

doi:10.3842/umzh.v76i9.7705

Serap Özcan Department of Mathematics, Faculty of Arts and Sciences, Kirklareli University, Turkey
Ayça Uruṣ Department of Mathematics, Institute of Natural Sciences, Kirklareli University, Turkey
Saad Ihsan Butt Department of Mathematics, COMSATS University Islamabad Lahore Campus, Pakistan

DOI: https://doi.org/10.3842/umzh.v76i9.7705

Keywords: log-Convex Functions, Harmonic log-Convex Functions, Multiplicative Calculus, Hermite-Hadamard Inequality

Abstract

UDC 517.5

We study the concept of multiplicative harmonic $s$-convex functions and establish Hermite–Hadamard integral inequalities for this class of functions. Furthermore, we derive a set of Hermite–Hadamard-type inequalities applicable to the product and quotient of multiplicative harmonic $s$-convex functions. In addition, we deduce new inequalities involving multiplicative integrals for the product and quotient of harmonic convex and multiplicative harmonic $s$-convex functions. Some results for the class of multiplicative harmonic convex functions are obtained as special cases of our results. The obtained results are verified by providing examples with included graphs.

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