10.30495/maca.2024.2017279.1093

Some inequalities of the Edmundson-Lah-Ribarič type for 3-convex functions with applications

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  • Rozarija Mikić1,
  • Đilda Pečarić2,
  • Josip Pečarić3,
  1. University of Rijeka, Faculty of Civil Engineering, Radmile Matejčić 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

Published in Issue 2024-01-01

How to Cite

Some inequalities of the Edmundson-Lah-Ribarič type for 3-convex functions with applications. (2024). Mathematical Analysis and Its Contemporary Applications, 6(1). https://doi.org/10.30495/maca.2024.2017279.1093

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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 type involving positive linear functionals that does 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 in order to obtain lower and upper bounds. Examples with Zipf-Mandelbrot law are used to illustrate the results. In addition, obtained results are utilized in constructing some families of exponentially convex functions and Stolarsky-type means.

Keywords

  • Jensen inequality,
  • Edmundson-Lah-Ribarič inequality,
  • 3-convex functions,
  • f-divergence,
  • Zipf-Mandelbrot law,
  • exponential convexity,
  • Stolarsky-type means
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References

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