On Integral Inequalities of Hermite‐Hadamard Type for s‐Geometrically Convex Functions

Abstract

The authors introduce the concept of thes-geometrically convex functions. By the well-known Hölder inequality, they establish some integral inequalities of Hermite-Hadamard type related to thes-geometrically convex functions and apply these inequalities to special means.

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.…”

Geometrically Relative Convex Functions

“…As a result of these activities, the concept of convexity has been extended and generalized in various directions using novel and innovative ideas see [1,6,7,9,10,11,12,13,14,15,16,18,19,22,23]. An important and significant generalization of the convex functions is the introduction of relative convex functions by Youness [6].…”

“…In recent years, much attention has been given to derive the Hermite-Hadamard type inequalities for various types of convex functions, see [1,2,4,17,19,20,21,22,23,24]. Motivated and inspired by the recent research going on in this field, we introduce and study a new class of relative convex functions, which is called the geometrically relative convex functions.…”

On Some Integral Inequalities for S-Geometrically Convex Functions and Their Applications

“…Recently, In [2], the concept of geometrically and s-geometrically convex functions was introduced as follows. Definition 1.3 [2] A function f : I ⊂ R + = (0, ∞) → R + is said to be a geometrically convex function if…”

“…Definition 1.3 [2] A function f : I ⊂ R + = (0, ∞) → R + is said to be a geometrically convex function if…”