Anita Matković

A variant of the Jensen-Mercer operator inequality for superquadratic functions

A variant of the Jensen-Mercer operator inequality for superquadratic functions, which is a refinement of the Jensen-Mercer operator inequality for convex functions, is proved. The result obtained is used to refine some comparison inequalities between operator power and quasi-arithmetic means of Mercers type.

On the Jensen-Steffensen inequality for generalized convex functions

Jensen-Steffensen type inequalities for P-convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of Čebyšev’s inequality and several variants of Hölder’s inequality with weights satisfying the conditions as in the Jensen-Steffensen inequality. A few well-known inequalities for quasi-arithmetic means are generalized.

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.

ON A VARIANT OF JENSEN'S INEQUALITY FOR FUNCTIONS WITH NONDECREASING INCREMENTS

Refinements of a variant of Jensens inequality for functions with nondecreasing increments are presented. Obtained results are used to prove refinements of related variants of Cebysevs inequality and Holders inequality.