Abstract
In this present case, we focus and explore the idea of a new family of convex function namely exponentialtype m–convex functions. To support this newly introduced idea, we elaborate some of its nice algebraicproperties. Employing this, we investigate the novel version of Hermite–Hadamard type integral inequality.Furthermore, to enhance the paper, we present several new refinements of Hermite–Hadamard (H−H) inequality.Further, in the manner of this newly introduced idea, we investigate some applications of specialmeans. These new results yield us some generalizations of the prior results in the literature. We believe, themethodology investigated in this paper will further inspire intrigued researchers.
Highlights
The theory of convexity is very important in the theoretical aspects of mathematicians and economists and for physicists
Mathematicians use this theory, to provide the solution of problems that arise in different branches of sciences
Areas of mathematics, as well as in other areas of science, economy, engineering, medicine, industry, and business. It is especially important in the study of optimization problems, where it is distinguished by a number of convenient properties
Summary
The theory of convexity is very important in the theoretical aspects of mathematicians and economists and for physicists. Areas of mathematics, as well as in other areas of science, economy, engineering, medicine, industry, and business It is especially important in the study of optimization problems, where it is distinguished by a number of convenient properties (for example, any minimum of a convex function is a global minimum, or the maximum is attained at a boundary point). This explains why there is a very rich theory of convex functions and convex sets. During the last few decades, the concept of convex analysis has played crucial and consequential role in the generalizations and extensions of theory of inequalities. A rich and meaningful literature on inequalities can be found for the convexity, see the references [10, 11, 12, 13, 14, 15, 16, 17, 18]
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