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Inequalities for Information Potentials and Entropies

Author

Listed:
  • Ana Maria Acu

    (Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5-7, RO-550012 Sibiu, Romania
    These authors contributed equally to this work.)

  • Alexandra Măduţa

    (Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

  • Diana Otrocol

    (Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
    Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, P.O. Box 68-1, 400110 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

  • Ioan Raşa

    (Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

Abstract

We consider a probability distribution p 0 ( x ) , p 1 ( x ) , … depending on a real parameter x . The associated information potential is S ( x ) : = ∑ k p k 2 ( x ) . The Rényi entropy and the Tsallis entropy of order 2 can be expressed as R ( x ) = − log S ( x ) and T ( x ) = 1 − S ( x ) . We establish recurrence relations, inequalities and bounds for S ( x ) , which lead immediately to similar relations, inequalities and bounds for the two entropies. We show that some sequences R n ( x ) n ≥ 0 and T n ( x ) n ≥ 0 , associated with sequences of classical positive linear operators, are concave and increasing. Two conjectures are formulated involving the information potentials associated with the Durrmeyer density of probability, respectively the Bleimann–Butzer–Hahn probability distribution.

Suggested Citation

  • Ana Maria Acu & Alexandra Măduţa & Diana Otrocol & Ioan Raşa, 2020. "Inequalities for Information Potentials and Entropies," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2056-:d:446836
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    References listed on IDEAS

    as
    1. Acu, Ana-Maria & Başcanbaz-Tunca, Gülen & Rasa, Ioan, 2021. "Information potential for some probability density functions," Applied Mathematics and Computation, Elsevier, vol. 389(C).
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    Cited by:

    1. Daniel Ioan Hunyadi & Oana-Adriana Ticleanu & Nicolae Constantinescu, 2022. "Optimal Elliptic-Curve Subspaces for Applications in Double-Authenticated Requests in Mobile Distributed Data Mining," Mathematics, MDPI, vol. 11(1), pages 1-14, December.

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