Some Hermite-Hadamard-Fejer type inequalities for harmonically convex functions via fractional integral

Abstract

In this paper, we gave the new general identity for differentiable functions. As a result of this identity some new and general inequalities for differentiable harmonically-convex functions are obtained.

Some new integral inequalities for n-times differentiable convex and concave functions

“…The classical Hermite-Hadamard inequality provides estimates of the mean value of a continuous convex or concave function. Hadamard's inequality for convex or concave functions has received renewed attention in recent years and a remarkable variety of refinements and generalizations have been found; for example see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. A function f : I ⊆ R → R is said to be convex if the inequality f (tx + (1 − t)y) tf (x) + (1 − t)f (y) , is valid for all x, y ∈ I and t ∈ [0, 1].…”

“…In references [2-4, 6, 13, 17, 19], readers can find some results about this issue. Many papers have been written by a number of mathematicians concerning inequalities for different classes of convex functions see for instance the recent papers [1,5,[7][8][9][10][11][12]14] and the references within these papers. Let 0 < a < b, throughout this paper we will use…”

Some New Integral Inequalities for $n$-Times Differentiable Trigonometrically Convex Functions

“…In references [2,4,8,14], readers can find some results about this issue. Many papers have been written by a number of mathematicians concerning inequalities for different classes of convex functions see for instance the recent papers [1,3,5,6] and the references within these papers.…”

Trapezoidal Type Fejér Inequalities Related to Harmonically Convex Functions and Application

“…where : [ , ] → R is convex and : [ , ] → R + is integrable and symmetric to = (2 /( + ))( ( ) = (1/(1/ + 1/ − 1/ )), ∀ ∈ [ , ]). For some other inequalities in connection with Fejér inequalities see [3][4][5][6][7][8] and the references therein.…”