engleski

Mercer and Wu-Srivastava generalizations of Steffensen's inequality

In this paper generalizations of Steffensen's inequality obtained by Pecaric, Mercer and Wu-Srivastava are related. Some of this generalizations are showed to be equivalent and using Wu-Srivastava refinement of Steffensen's inequality refined versions of Pecaric and Mercer's results are obtained. Using Wu-Srivastava sharpened and generalized version of Mercer's result sharpened version of generalization given by Pecaric is obtained. Furthermore, weaker conditions for some generalizations and refinements are obtained. Moreover, functionals defined as the difference between the left-hand and the right-hand side of generalizations and refinements of Steffensen's inequality are studied. New Stolarsky type means, using several families of exponentially convex functions, related to defined functionals are generated.

Steffensen inequality; monotonic functions; weaker conditions; exponential convexity; Stolarsky type means

nije evidentirano