Hermite-Hadamard type inequalities for \(n\)-polynomial generalized convex functions of Raina type and some related inequalities

Abstract

In this paper, we introduce the concept of a new family of convex functions namely n-polynomial generalized convex functions of Raina type. We investigate the algebraic properties of a newly introduced idea and discuss their connections with convex functions. Furthermore, we establish the new version of Hermite–Hadamard and some refinements of Hermite-Hadamard type inequalities this class of functions. Finally, we investigate some applications to special means of real numbers. Results obtained in this paper can be viewed as a significant improvement of previously known results and also may stimulate and energize for further activities in this research area field.