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