Generalized Jensen-Mercer Inequality for Functions with Nondecreasing Increments

Abstract

In the year 2003, McD Mercer established an interesting variation of Jensen’s inequality and later in 2009 Mercer’s result was generalized to higher dimensions by M. Niezgoda. Recently, Asif et al. has stated an integral version of Niezgoda’s result for convex functions. We further generalize Niezgoda’s integral result for functions with nondecreasing increments and give some refinements with applications. In the way, we generalize an important result, Jensen-Boas inequality, using functions with nondecreasing increments. These results would constitute a valuable addition to Jensen-type inequalities in the literature.

Untitled

“…Due to its fundamental importance, over the year it has been generalized to various context. There are given numerous variants, generalizations and refinements of Jensens inequalities for reference see [2], [3], [8], [9], [10], [11], [13], [14], [17], [18], [19], [20], [21], [22], [34], [36], [39], [40]. Throughout this paper, we assume I is an interval in R and we assume w = (w 1 , .…”

Generalization and Refinements of Jensen Inequality

“…Due to its fundamental importance, over the year it has been generalized to various context. There are given numerous variants, generalizations and refinements of Jensens inequalities for reference see [2], [3], [8], [9], [10], [11], [13], [14], [17], [18], [19], [20], [21], [22], [34], [36], [39], [40]. Throughout this paper, we assume I is an interval in R and we assume w = (w 1 , .…”

Untitled

“…Due to its fundamental importance, over the year it has been generalized to various context. There are given numerous variants, generalizations and refinements of Jensens inequalities for reference see [2], [3], [8], [9], [10], [11], [13], [14], [17], [18], [19], [20], [21], [22], [34], [36], [39], [40]. Throughout this paper, we assume I is an interval in R and we assume w = (w 1 , .…”