Hadamard integral inequality for the class of semi-harmonically convex functions

Abstract

In this paper, we introduce the concept of right semi-harmonically [Formula: see text]-convex, (RHS [Formula: see text]-convex) function by the inequality [Formula: see text] and also left semi-harmonically [Formula: see text]-convex, (LHS [Formula: see text]-convex) [Formula: see text] where [Formula: see text] and [Formula: see text] are two geodesic arcs. Then, we will find some refinements of Hadamard integral inequality for semi-harmonically [Formula: see text]-convex functions in the case of Sugeno and Lebesque integral.