On Levinson's inequality

Alfred Witkowski

Abstract


We give a very simple proof of the classical Levinson inequality and generalise the result by Mercer.

Keywords


3-convex; Levinson inequality.

Mathematics Subject Classification


26D15

References


Boas, R.P. and D.V. Widder. "Functions with positive differences." Duke Math. J. 7 (1940): 496-503.

Bullen, P.S. "An inequality of N. Levinson." Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 412-460 (1973): 109-112.

Levinson, N. "Generalization of an inequality of Ky Fan." J. Math. Anal. Appl. 8 (1964): 133-134.

Mercer, A.McD. "Short proofs of Jensen’s and Levinson’s inequalities." Math. Gazette 94 (2010): 492-495.

Pecaric, J.E. "On Levinson’s inequality." Real Anal. Exchange 15 (1989/90): 710-712.

Popoviciu, T. "Sur une inégalité de N. Levinson." Mathematica (Cluj) 6 (1964): 301-306.


Full Text: PDF

Download statistics: 2623

Licencja Creative Commons
This article by Alfred Witkowski is governed by the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported licence.


e-ISSN: 2300-133X, ISSN: 2081-545X

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more

The Journal is indexed in:
and others see Abstracting and Indexing list

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019

Deklaracja dostępności cyfrowej