Hermite–Hadamard Type Inequalities via Generalized Harmonic Exponential Convexity and Applications

Abstract

In this work, we introduce the idea and concept of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>m</a:mi> </a:math> –polynomial <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>p</c:mi> </c:math> –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.