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Journal of Function Spaces
Volume 2014 (2014), Article ID 428030, 10 pages
http://dx.doi.org/10.1155/2014/428030
Research Article

Generalized Steffensen Type Inequalities Involving Convex Functions

Faculty of Textile Technology, University of Zagreb, Prilaz Baruna Filipovića 28a, 10000 Zagreb, Croatia

Received 14 April 2014; Accepted 16 July 2014; Published 5 August 2014

Academic Editor: Hugo Leiva

Copyright © 2014 Josip Pečarić and Ksenija Smoljak Kalamir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.