Generalized geometrically convex functions and inequalities

Abstract

In this paper, we introduce and study a new class of generalized functions, called generalized geometrically convex functions. We establish several basic inequalities related to generalized geometrically convex functions. We also derive several new inequalities of the Hermite-Hadamard type for generalized geometrically convex functions. Several special cases are discussed, which can be deduced from our main results.

More results on integral inequalities for strongly generalized ( ϕ , h , s ) $( \phi,h,s )$ -preinvex functions

“…A huge speculation of convex functions is that of invex functions presented in [2]. The fundamental properties of the preinvex functions and their use in optimization and mathematical programming issues have been considered in [3][4][5]. It is realized that the preinvex functions and invex sets may not be convex functions and convex sets, respectively.…”

Generalized r-Convex Functions and Integral Inequalities

“…The generalized convex functions are nonconvex functions. For recent developments, see [3,6,[18][19][20][21][25][26][27][28][29][30][31] and the references therein. Inspired and motivated by the ongoing research, we introduce a new class of generalized convex functions, which is called generalized r-convex functions.…”

Integral Inequalities via Generalized Geometrically r-Convex Functions

“…which is known as Hermite-Hadamard inequality and is one of the most important inequality. In recent years, much attention has been given to derive the Hermite-Hadamard type inequalities for various types of convex functions, see [6,11,14,15,[22][23][24][25][26][27][28][29][30][31][32][33].…”

“…al [11] introduced the class of r-convex functions. Several authors have derived Hermite-Hadamard type inequalities for various classes of r-convex functions, see [22,28,[31][32][33]. Gordji et al [9] introduced an important class of convex functions involving the bifunction, which is called generalized(ϕ-convex) convex function.…”