A parameter-dependent refinement of the discrete Jensen's inequality for convex and mid-convex functions

Abstract

In this paper, a new parameter-dependent refinement of the discrete Jensen's inequality is given for convex and mid-convex functions. The convergence of the introduced sequences is also studied. One of the proofs requires an interesting convergence theorem with probability theoretical background. We apply the results to define some new quasi-arithmetic and mixed symmetric means and study their monotonicity and convergence.

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 , .…”