Rozarija Mikić; Đilda Pečarić; Josip Pečarić
Abstract
In this paper, we study 3-convex functions, which are characterized by the third-order divided differences, and for them, we derive a class of inequalities of the Jensen and Edmundson-Lah-Ribarič ...
Read More
In this paper, we study 3-convex functions, which are characterized by the third-order divided differences, and for them, we derive a class of inequalities of the Jensen and Edmundson-Lah-Ribarič type involving positive linear functionals that do not require convexity in the classical sense. A great number of theoretic divergences, i.e. measures of distance between two probability distributions, are special cases of Csiszár f-divergence for different choices of the generating function f. In the second part of this paper, we apply our main results to the generalized f-divergence functional to obtain lower and upper bounds. Examples of Zipf–Mandelbrot law are used to illustrate the results. In addition, the obtained results are utilized in constructing some families of exponentially convex functions and Stolarsky-type means.
