M. Klaričić Bakula

Hadamard-type inequalities for s-convex functions

In this paper we establish some new inequalities for differentiable functions based on concavity and s-convexity. We also prove several Hadamard-type inequalities for products of two convex and s-convex functions.

On the converse Jensen inequality

We give a survey on the converse Jensen inequality and we show that several recently published inequalities are simple consequences of certain long time known results. We also give a new refinement of the converse Jensen inequality as well as improvements of some related results.

GENERALIZED HADAMARD'S INEQUALITIES BASED ON GENERAL EULER 4-POINT FORMULAE

We present a general closed 4-point quadrature rule based on Euler-type identities. We use this rule to prove a generalization of Hadamards inequalities for (2/-)-convex functions (T > 1).

Variants of Čebyšev's inequality with applications

Several variants of Čebyševs inequality for two monotonic-tuples and also nonnegative-tuples monotonic in the same direction are presented. Immediately after that their refinements of Ostrowskis type are given. Obtained results are used to prove generalizations of discrete Milnes inequality and its converse in which weights satisfy conditions as in the Jensen-Steffensen inequality.