Generalised Hermite-Hadamard type inequalities for \((s,r)\)-convex functions in mixed kind with applications

Volume 30, Issue 4, pp 372--380 http://dx.doi.org/10.22436/jmcs.030.04.06

Publication Date: February 18, 2023 Submission Date: December 15, 2022 Revision Date: January 16, 2023 Accteptance Date: January 30, 2023

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Authors

F. Mehmood - Department of Mathematics, Samarkand State University, Samarkand 140104, Uzbekistan. - Department of Mathematics, Dawood University of Engineering and Technology, Karachi-74800, Pakistan. F. Nawaz - Department of Mathematics, Dawood University of Engineering and Technology, Karachi-74800, Pakistan. A. Soleev - Department of Mathematics, Samarkand State University, Samarkand 140104, Uzbekistan.

Abstract

In this article, some generalized inequalities of the Hermite-Hadamard type for functions whose modulus of the derivatives are \((s,r)\)-convex in mixed kind and applications for probability theory and numerical integration are given. Various established results of different articles would be recaptured as special cases. We also provide special cases of the class of \((s,r)\)-convex function on several choices of \(s,r\).

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Keywords

• Convex function
• Hermite-Hadamard inequality
• Hölder inequality
• power-mean inequality
• numerical integration
• probability density function

MSC

•  26A33
•  26A51
•  26D15
•  26D99
•  47A30
•  33B10

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