Ksenija Smoljak Kalamir

MEASURE THEORETIC GENERALIZATION OF PECARI ˇ C, ´ MERCER AND WU-SRIVASTAVA RESULTS

In this paper generalizations of Steffensen’s inequality obtained by Pecaric, Mercer and Wu-Srivastava are further extended in a measure theoretic sense. Motivated by Wu and Srivastava’s refined and sharpened version of Mercer’s result related inequalities for positive Borel measures are obtained.

Generalized Steffensen Type Inequalities Involving Convex Functions

In this paper generalized Steffensen type inequalities related to the class of functions that are “convex at point ” are derived and as a consequence inequalities involving the class of convex functions are obtained. Moreover, linear functionals from the difference of the right- and left-hand side of the obtained generalized inequalities are constructed and new families of exponentially convex functions related to constructed functionals are derived.

Bellman–Steffensen type inequalities

In this paper some Bellman–Steffensen type inequalities are generalized for positive measures. Using sublinearity of a class of convex functions and Jensen’s inequality, nonnormalized versions of Steffensen’s inequality are obtained. Further, linear functionals, from obtained Bellman–Steffensen type inequalities, are produced and their action on families of exponentially convex functions is studied.

Generalizations of Steffensen's inequality via some Euler-type identities

Abstract Using Euler-type identities some new generalizations of Steffensen’s inequality for n–convex functions are obtained. Moreover, the Ostrowski-type inequalities related to obtained generalizations are given. Furthermore, using inequalities for the Čebyšev functional in terms of the first derivative some new bounds for the remainder in identities related to generalizations of Steffensen’s inequality are proven.

On some Bounds for the Parameter λ in Steffensen's Inequality

The object is to obtain weaker conditions for the parameter in Steffensens inequality and its generalizations and refinements additionally assuming nonnegativity of the function f . Furthermore, we contribute to the investigation of the Bellman-type in- equalites establishing better bounds for the parameter .