On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind

Converses of the Jensen inequality derived from the Green functions with applications in information theory

“…and taking 1 p as a power. Also, using the fact that x − ≤ (x − ) for 0 ≤ ≤ x and ∈ [0, 1], we deduce (12).…”

“…7 Some of the most important mathematical inequalities are obtained by using the idea of convexity. [8][9][10][11][12] Over 100 years ago, Jensen introduced the inequality for convex function which is paramount and extensively used inequality in the literature for application purpose. In the literature of inequalities, Jensen inequality is of pivotal importance because other classical inequalities, eg, Ky-Fan, Hölder, Levinson's, Beckenbach-Dresher, Minkowski's, arithmetic-geometric, and Young's inequalities, can be deduced from this inequality.…”

Generalization of Hermite-Hadamard Type Inequalities via Conformable Fractional Integrals

“…Recently, the mean value theory has been the subject of intensive research, and many remarkable inequalities and properties for various bivariate means can be found in the literature [28][29][30][31][32][33].…”

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 .…”