Generalized Levinson's inequality and exponential convexity

• Autorzy: Pecaric J. , Praljak M. , Witkowski A.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.3.397

• Języki publikacji: EN

Abstrakty

EN

We give a probabilistic version of Levinson's inequality under Mercer's assumption of equal variances for the family of 3-convex functions at a point. We also show that this is the largest family of continuous functions for which the inequality holds. New families of exponentially convex functions and related results are derived from the obtained inequality.

Słowa kluczowe

EN

Levinson's inequality; exponential convexity

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 3
• Strony: 397--410
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Pecaric J.

• Faculty of Textile Technology University of Zagreb Prilaz baruna Filipovica 28a, 10000 Zagreb, Croatia

autor

Praljak M.

• Faculty of Food Technology and Biotechnology University of Zagreb Pierottijeva 6, 10000 Zagreb, Croatia

autor

Witkowski A.

• Institute of Mathematics and Physics UTP University of Science and Technology al. prof. Kaliskiego 7, 85-796 Bydgoszcz, Poland

Bibliografia

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• [2] M. Anwar, J. Pećarić, On logarithmic convexity for Ky-Fan inequality, J. Inequal. Appl. 2008, Art. ID 870950, 4 pp.
• [3] LA. Baloch, J. Pećarić, M. Praljak, Generalization of Levinson's inequality, J. Math. Inequal., accepted.
• [4] P.S. Bullen, An inequality of N. Levinson, Univ. Beograd Publ. Elektrotehm. Fak. Ser. Mat. Fiz. 421-460 (1973), 109-112.
• [5] N. Levinson, Generalization of an inequality of Ky Fan, J. Math. Anal. Appl. 8 (1964), 133-134.
• [6] A. McD. Mercer, Short proof of Jensen's and Levinson's inequalities, Math. Gazette 94 (2010), 492-495.
• [7] J. Pećarić, On an inequality of N. Levinson, Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 678-715 (1980), 71-74.
• [8] J. Pećarić, J. Perić, Improvements of the Giaccardi and the Petrovic inequality and related Stolarsky type means, An. Univ. Craiova Ser. Mat. Inform. 39 (2012), 65-75.
• [9] J. Pećarić, F. Proschan, Y.L. Tong, Convex Functions, Partial Orderings, and Statistical Applications, Academic Press Inc., 1992.
• [10] T. Popoviciu, Sur une inegalite de N. Levinson, Mathematica (Cluj) 6 (1964), 301-306.
• [11] A. Witkowski, On Levinson's inequality, Ann. Univ. Paed. Cracov. Stud. Math. 12 (2013), 59-67.
• [12] A. Witkowski, On Levinson's inequality, RGMIA Research Report Collection 15 (2012), Article 68.