Conformable Integral Inequalities of the Hermite-Hadamard Type in terms of GG- and GA-Convexities

Abstract

In the article, we present several conformable fractional integrals’ versions of the Hermite-Hadamard type inequalities for GG- and GA-convex functions and provide their applications in special bivariate means.

Association of Jensen’s inequality for s-convex function with Csiszár divergence

“…Convex function has wide applications in pure and applied mathematics, physics, and other natural sciences [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]; it has many important and interesting properties [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] such as monotonicity, continuity, and differentiability. Recently, many generalizations and extensions have been made for the convexity, for example, s-convexity [38], strong convexity [39][40][41], preinvexity [42], GA-convexity [43], GG-convexity [44], Schur convexity [45][46][47][48]…”

Inequalities Involving Conformable Approach for Exponentially Convex Functions and Their Applications

“…Many upper and lower bounds for the mean value of a convex function can be derived by use of inequality (1). Recently, the generalizations, improvements, refinements, extensions, and variants for Hermite-Hadamard inequality (1) can be found in the literature [16][17][18][19].…”

Petrović-Type Inequalities for Harmonic h-convex Functions

“…It is well known that the convex (concave) functions have wide applications in pure and applied mathematics , many remarkable properties and inequalities can be found in the literature via the theory of convexity. Recently, a great deal of generalizations, extensions, and variants have been made for convexity, for example, GA-convexity [49], GG-convexity [50], -convexity [51,52], preinvex convexity [53], strong convexity [54][55][56][57], Schur convexity [58][59][60], and others [61][62][63][64][65][66][67].…”