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.
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