Monotonicity rule for the quotient of two functions and its application

Abstract

In the article, we provide a monotonicity rule for the function , where is a positive differentiable and decreasing function defined on (), and and are two real power series converging on such that the sequence is increasing (decreasing) with and for all . As applications, we present new bounds for the complete elliptic integral () of the second kind.

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.…”

Majorization theorems for strongly convex functions

“…Remark 2. 10 We clearly see that inequalities (2.7), (2.8), and (2.9) are the improvements of the corresponding inequalities given in [84].…”

“…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.…”

Discrete majorization type inequalities for convex functions on rectangles

“…, y n ) ∈ I and ·, · is the ordinary inner product in R n . Convex functions have many important applications in mathematics, physics, statistics and engineering [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Currently, many refinements, variants, generalizations and extensions for the convexity can be found in the literature .…”