On Jensen’s type inequalities via generalized majorization inequalities

Abstract

In this paper, we give generalizations of Jensen's, Jensen-Steffensen's and converse of Jensen's inequalities by using generalized majorization inequalities. We also present Grüss and Ostrowski-type inequalities for the generalized inequalities.

Generalization of Favard’s and Berwald’s Inequalities for Strongly Convex Functions

“…Since Ψ is strongly convex function with respect to c, therefore Ψ(x) − cx 2 is convex function. Applying this convex function on [28, Corollary 2.4], we deduce (22), (23), (24) and (25).…”

Refinements of Majorization Inequality Involving Convex Functions via Taylor’s Theorem with Mean Value form of the Remainder

“…Applying an additional condition ∑ n i=1 i ν i ≤ ∑ n i=1 i ϑ i to inequality (12), we obtain the following result. Corollary 1.…”

“…A survey of the applications of majorization and relevant results can be found in the monograph of Marshall and Olkin [2]. Recently, the authors have given considerable attention to the generalizations and applications of the majorization and related inequalities, for details, we refer the reader to our papers [3][4][5][6][7][8][9][10][11][12][13].…”

Bivariate Montgomery identity for alpha diamond integrals

“…Let where p(x, t) is called Peano kernel, defined in [17]. Some applications of Montgomery identity in the form of inequalities can be found in [13,15,16]. Dragomir et al extended it for a function of two variables on the real line [12] in the following form:…”