Vera Čuljak

Schur-Convexity of Averages of Convex Functions

The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results. First, Schur-convexity of the generalized integral and weighted integral quasiarithmetic mean is studied. Relation to some already published results is established, and some applications of the extended result are given. Furthermore, Schur-convexity of functions connected to the Hermite-Hadamard inequality is investigated. Finally, some results on convexity and Schur-convexity involving divided difference are considered.

On Jensen-McShane’s inequality

A sequence of inequalities which include McShane’s generalization of Jensen’s inequality for isotonic positive linear functionals and convex functions are proved and compared with results in [3]. As applications some results for the means are pointed out. Moreover, further inequalities of Hölder type are presented.

On discrete and continuous wirtinger inequalities

We shall present several generalizations of discrete Wirtingers inequality, and establish their continuous analogs.

On some inequalities for convex functions of higher order II

In this paper we prove some inequalities for convex function of a higher order. The well known Hermite interpolating polynomial leads us to a converse of Jensen inequality for a regular, signed measure and, as a consequence, a generalization of Hadamard and Petrovi cs inequalities. Also, we obtain a new upper bound for the error function of the Hermite interpolating polynomial je H (x)j in terms of kf (n) k , resulting in a generalization of Mahajani inequality for diierent norm :

On Some Integral and Tail Inequalities Motivated by Kesava Menon's Theorem

Kesava Menons classical inequality is connected with the tails of Taylors series. In this paper the original statements are improved, under the same or weaker conditions on functions involved.