Abstract
In this work, we introduce the idea and concept of m –polynomial p –harmonic exponential type convex functions. In addition, we elaborate the newly introduced idea by examples and some interesting algebraic properties. As a result, several new integral inequalities are established. Finally, we investigate some applications for means. The amazing techniques and wonderful ideas of this work may excite and motivate for further activities and research in the different areas of science.
Highlights
Theory of convexity present an active, fascinating, and attractive field of research and played prominence and amazing act in different fields of science, namely, mathematical analysis, optimization, economics, finance, engineering, management science, and game theory
Motivated and inspired by the ongoing activities and research in the convex analysis field, we found out that there exists a special class of function known as exponential convex function, and nowadays, a lot of people working are in this field [12, 13]
We have introduced and investigated some algebraic properties of a new class of functions, namely, m–poly p–harmonic exp convex
Summary
Theory of convexity present an active, fascinating, and attractive field of research and played prominence and amazing act in different fields of science, namely, mathematical analysis, optimization, economics, finance, engineering, management science, and game theory. It is well known that the harmonic mean is the special case of power mean It is often used for the situations when the average rates is desired and have a lot of applications in different field of sciences which are statistics, computer science, trigonometry, geometry, probability, finance, and electric circuit theory. Awan et al [11] keeping his work on generalizations, Journal of Function Spaces introduced a new class called n–polynomial harmonically convex function. Geo et al [17] introduced n–polynomial harmonic exponential type convex functions. The fruitful benefits and applications of exponential type convexity is used to manipulate for statistical learning, information sciences, data mining, stochastic optimization and sequential prediction [7, 18, 19] and the references therein. We need the following necessary known definitions and literature
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