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Entropy results for Levinson-type inequalities via Green functions and Hermite interpolating polynomial

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Abstract

In this work, Levinson type inequalities involving two types of data points are proved using Green functions and the Hermite interpolating polynomial for the class of n-convex functions. In seek of applications to information theory some estimates for new functionals are obtained, based on \(\mathbf {f}\)-divergence. Moreover, some inequalities involving Shannon entropies are deduced as well.

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Acknowledgements

The authors wish to thanks the anonymous referees for their very careful reading of the manuscript and fruitful comments and suggestions. The research of the 4th author is supported by the Ministry of Education and Science of the Russian Federation (the Agreement number No. 02.a03.21.0008).

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Authors and Affiliations

  1. Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan

    Muhammad Adeel & Khuram Ali Khan

  2. Department of Mathematics, University of Central Punjab, Lahore, Pakistan

    Muhammad Adeel

  3. Department of Media and Communication, University North, Trg dr. Žarka Dolinara 1, Koprivnica, 242, Croatia

    Đilda Pečarić

  4. RUDN University, Miklukho-Maklaya str. 6, 117198, Moscow, Russia

    Josip Pečarić

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  1. Muhammad Adeel
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  2. Khuram Ali Khan
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  3. Đilda Pečarić
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  4. Josip Pečarić
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Correspondence to Muhammad Adeel.

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Adeel, M., Khan, K.A., Pečarić, Đ. et al. Entropy results for Levinson-type inequalities via Green functions and Hermite interpolating polynomial. Aequat. Math. 96, 1–16 (2022). https://doi.org/10.1007/s00010-021-00845-3

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