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.


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