The Hermite-Hadamard type inequality and its estimations via generalized convex functions of Raina type

Year 2021, Volume: 1 Issue: 1, 32 - 43, 30.09.2021

Muhammad Tarıq Hijaz Ahmad Soubhagya Kumar Sahoo

https://doi.org/10.53391/mmnsa.2021.01.004

Cited By: 11

Abstract

The theory of convexity plays an important role in various branches of science and engineering. The main objective of this work is to introduce the idea of a generalized convex function by unifying s-type m-convex function and Raina type function. In addition, some beautiful algebraic properties and examples are discussed. Applying this new definition, we explore a new sort of Hermite-Hadamard inequality. Furthermore, to enhance the paper we investigate several new estimations of Hermite-Hadamard type inequality. The concepts and tools of this paper may invigorate and revitalize for additional research in this mesmerizing and absorbing field of mathematics.

Keywords

Convex function, m-convex function, s-type convex function, Hölder, improved power-mean integral inequality

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