On Levinson's inequality involving averages of 3-convex functions

By using the Levinson inequality we give the extension for 3-convex functions of Wulbert's result from Favard's Inequality on Average Values of Convex Functions, Math. Comput. Model. 37 (2003), 1383{1391. Also, we obtain inequalities with divided differences, and as a consequence, the convexity of higher order for function defined by divided difference is proved. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking at linear functionals associated with these new inequalities.

Favard’s inequality for pseudo-integral

The purpose of this paper is to generalize Favard’s inequality for pseudo-integral. We consider two cases for the real semiring [Formula: see text], when pseudo-operations are defined by a continuous and monotone function and when the pseudo-addition is sup operation and the pseudo-multiplication is generated by a continuous and monotone function.

EXPONENTIAL CONVEXITY OF THE FAVARD'S INEQUALITY AND RELATED RESULTS

A b s t r a c t: In this paper we prove positive semi-definiteness of matrices generated by differences deduced from unweighted and weighted Favard's inequality. This implies a surprising property of exponential convexity of this differences which allows us to deduce Gram's, Lyapunov's and Dresher's types of inequalities for this differences.