Generalized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral

Abstract

In this paper, we give a new identity for differentiable and GA-convex functions. As a result of this identity, we obtain some new fractional integral inequalities for differentiable GA-convex functions.

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].…”

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

“…Işcan and S. Turhan used this identity for GA-convex functions and obtain generalized new inequalities. In this paper, we established a new inequality similar to inequality in [12] and then we obtained some new and general integral inequalities for differentiable harmonically-convex functions using this lemma. The following sections, let the notion,…”

“…Then in [12]İ. Işcan and S. Turhan used this identity for GA-convex functions and obtain generalized new inequalities.…”

“…For more results on (1) which provide new proof, significantly extensions, generalizations, refinements, counterparts, new Hermite-Hadamard-type inequalities and numerous applications, we refer the interested reader to [2,3,5,6,8,9,12,13,15,16] and the references there in.…”

Some new integral inequalities for n-times differentiable log-convex functions

“…Convexity theory has appeared as a powerful technique to study a wide class of unrelated problems in pure and applied sciences. For some inequalities, generalizations and applications concerning convexity see [6,9,10,11]. Recently, in the literature there are so many papers about n-times differentiable functions on several kinds of convexities.…”