Quadratic transformation inequalities for Gaussian hypergeometric function

Abstract

In the article, we present several quadratic transformation inequalities for Gaussian hypergeometric function and find the analogs of duplication inequalities for the generalized Grötzsch ring function.

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

“…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][49], and others [50][51][52][53][54]. In particular, many remarkable inequalities can be found in the literature [55][56][57][58][59][60][61][62][63][64][65][66][67] via the convexity theory.…”

On approximating the quasi-arithmetic mean

“…In particular, K(r) and E(r) are the special cases of the Gaussian hypergeometric function [17][18][19][20][21][22][23][24][25][26] as follows: is the shifted factorial function and Γ (x) = ∞ 0 t x-1 e -t dt (x > 0) is the classical gamma function [27][28][29][30][31][32][33][34][35].…”

Majorization theorems for strongly convex functions

“…Convexity is one the most important, natural, and fundamental concepts in mathematics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Convex functions were proposed by Jensen over 100 years ago.…”