Some Hermite-Hadamard type inequalities for n-time differentiable "Equation missing" -convex functions

Abstract

In the paper, the famous Hermite-Hadamard integral inequality for convex functions is generalized to and refined as inequalities for n-time differentiable functions which are (α, m)-convex. MSC: Primary 26D15; secondary 26A51; 41A55

Hermite-Hadamard type inequalities for product of GA-convex functions via Hadamard fractional integrals

“…In time, Hermite-Hadamrd inequality is developed other kinds of convex functions. For some results which generalize, improve, and extend the Hermite-Hadamard inequality see [1,7,10,18,20] and references therein.…”

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].…”

Integral Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>s</i>-Convex

“…new inequalities of Hermite-Hadamard pe inequalities were created in, for example, [8][9][10][11][12][13][14][15][16][17], especially the monographs [18,19], and related references therein.…”