Some Companions of Fejér-Type Inequalities for Harmonically Convex Functions

Abstract

In this paper, we present some mappings defined over 0,1 related to the Fejér-type inequalities that have been established for harmonically convex functions. As a consequence, we obtain companions of Fejér-type inequalities for harmonically convex functions by using these mappings. Properties of these mappings are discussed, and consequently, we obtain refinement inequalities of some known results.

Fejér-Type Inequalities for Harmonically Convex Functions and Related Results

“…and then integrating over κ 1 , 2κ 1 κ 2 κ 1 +κ 2 , we get that N 1 (κ 1 ) ≤ N 1 (κ 2 ) for κ 1 , κ 2 ∈ [0, 1] with κ1 < κ 2 . Hence, N 1 is increasing on [0, 1] and thus the inequalities (22) follow.…”