Novel Refinements via n –Polynomial Harmonically s –Type Convex Functions and Application in Special Functions

In this work, we introduce the idea of n –polynomial harmonically s –type convex function. We elaborate the new introduced idea by examples and some interesting algebraic properties. As a result, new Hermite–Hadamard, some refinements of Hermite–Hadamard and Ostrowski type integral inequalities are established, which are the generalized variants of the previously known results for harmonically convex functions. Finally, we illustrate the applicability of this new investigation in special functions (hypergeometric function and special mean of real numbers).