Julije Jakšetić

On Some Improvements of the Jensen Inequality with Some Applications

An improvement of the Jensen inequality for convex and monotone function is given as well as various applications for mean. Similar results for related inequalities of the Jensen type are also obtained. Also some applications of the Cauchy mean and the Jensen inequality are discussed.

On a global upper bound for Jensen's inequality

In two recent papers a global upper bound is derived for Jensens inequality for weighted finite sums. In this paper we generalize this result on positive normalized functionals.

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.

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.