A refined class of harmonically convex functions and Bullen-Mercer-type inequalities

Volume 39, Issue 4, pp 500--521 https://dx.doi.org/10.22436/jmcs.039.04.06

Publication Date: May 21, 2025 Submission Date: November 17, 2024 Revision Date: December 04, 2024 Accteptance Date: February 28, 2025

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Authors

S. Ali - Department of Mathematics, University of Sargodha, P.O. Box 40100, Sargodha, Pakistan. M. Samraiz - Department of Mathematics, University of Sargodha, P.O. Box 40100, Sargodha, Pakistan. S. Naheed - Department of Mathematics, University of Sargodha, P.O. Box 40100, Sargodha, Pakistan. M. Vivas-Cortez - FRACTAL (Fractional Research Convexity Analysis and Their Laboratory Applications, Naturales y Ambientales, Facultad de Ciencias Exactas, Pontificia Universidad Católica del Ecuador, Ecuador. Y. Elmasry - Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61466, Saudi Arabia.

Abstract

This paper introduces a new class of convex functions namely the harmonic inverse sine trigonometric convex (HISTC) functions defined over a real vector space, which exhibits unique refinement characteristics. We provide a detailed mathematical formulation and analyze its algebraic properties. Using this refined class, we establish an identity that serves as a foundation to establish refinements of Bullen-Mercer-type inequalities. The derived results are authenticated through 2D and 3D graphs as well as numerical analysis. Additionally, we demonstrate applications of our findings by their use in analyzing means. By discussing the limiting cases, we prove that the main results are general comparing those in the existing literature.

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Keywords

• Harmonically inverse sine trigonometric convex functions
• Bullen-Mercer-type inequality
• Hölder’s inequality
• applications to special means

MSC

•  26A51
•  26D15

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