Abstract
We consider a family of probability distributions depending on a real parameter x, and study the logarithmic convexity of the sum of the squared probabilities. Applications concerning bounds and concavity properties of Rényi and Tsallis entropies are given. Finally, some extensions and an open problem are presented.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abel, U., Gawronski, W., Neuschel, Th: Complete monotonicity and zeros of sums of squared Baskakov functions. Appl. Math. Comput. 258, 130–137 (2015)
Altomare, F., Campiti, M.: Korovkin-Type Approximation Theory and Its Applications. de Gruyter, Berlin (1994)
Bărar, A., Mocanu, G., Raşa, I.: Bounds for some entropies and special functions. Carpathian J. Math. (2018). arXiv:1801.05003v1, 8 Jan 2018
Berdysheva, E.: Studying Baskakov–Durrmeyer operators and quasi-interpolants via special functions. J. Approx. Theory 149, 131–150 (2007)
Gonska, H., Raşa, I., Rusu, M.-D.: Chebyshev-Grüss-type inequalities via discrete oscillations. Bul. Acad. Stiinte Repub. Mold. Mat. 1(74), 63–89 (2014). arXiv:1401.7908 [math.CA]
Nikolov, G.: Inequalities for ultraspherical polynomials. Proof of a conjecture of I. Raşa. J. Math. Anal. Appl. 418, 852–860 (2014)
Raşa, I.: Entropies and Heun functions associated with positive linear operators. Appl. Math. Comput. 268, 422–431 (2015)
Raşa, I.: Special functions associated with positive linear operators. arXiv:1409.1015v2 (2014)
Raşa, I.: The index of coincidence for the binomial distribution is log-convex. arXiv:1706.05178v1, 16 Jun 2017
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Professor Heiner Gonska on the occasion of his 70th birthday.
Rights and permissions
About this article
Cite this article
Raşa, I. Convexity Properties of Some Entropies. Results Math 73, 105 (2018). https://doi.org/10.1007/s00025-018-0868-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00025-018-0868-8