Document Type : Original Article


1 University of Rijeka, Faculty of Civil Engineering, Radmile Matejcic 3, 51 000 Rijeka, Croatia

2 Catholic University of Croatia, Ilica 242, 10 000 Zagreb, Croatia

3 Croatian Academy of Sciences and Arts, 10 000 Zagreb, Croatia



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.


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