Abstract
Some authors introduced the concepts of the harmonically arithmetic convex functions and establish some integral inequalities of Hermite Hadamard Fejér type related to the harmonically arithmetic convex functions. In this paper, a mapping M(t) is considered to get some preliminary results and a new trapezoidal form of Fejér inequality related to the harmonically arithmetic convex functions. By using a mapping M(t), the new theorems and corollaries are obtained. Taking advantage of these, applications were given for some real number averages.
Highlights
Fejer proved the following integral inequalities known in the literature as Fejer inequality [1, 2]: f
In [9], Hwang found out the Fejer trapezoidal inequality related to convex functions as follows: Theorem 1
We have obtained the new theorem and corollary about Hermite Hadamard Fejer type inequality for the both harmonically convex functions. We use this lemma for harmonically convex function and motivated by above works and results we consider a mapping M(t) and obtain some introductory properties related to it
Summary
A mapping M(t) is considered to get some preliminary results and a new trapezoidal form of Fejer inequality related to the harmonically arithmetic convex functions. In [9], Hwang found out the Fejer trapezoidal inequality related to convex functions as follows: Theorem 1. If the mapping |f| is convex on [a, b], the following inequality holds: If |f|q is convex on [a, b], q > 1, the following inequality holds:
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