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Abstract and Applied Analysis
Volume 2014, Article ID 859696, 6 pages
Research Article

A Korovkin Type Approximation Theorem and Its Applications

Department of Mathematics and Computer Application, College of Sciences, University of Al-Muthanna, Samawa, Iraq

Received 28 January 2014; Accepted 20 March 2014; Published 17 April 2014

Academic Editor: Ivanka Stamova

Copyright © 2014 Malik Saad Al-Muhja. 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.


We present a Korovkin type approximation theorem for a sequence of positive linear operators defined on the space of all real valued continuous and periodic functions via A-statistical approximation, for the rate of the third order Ditzian-Totik modulus of smoothness. Finally, we obtain an interleave between Riesz's representation theory and Lebesgue-Stieltjes integral-i, for Riesz's functional supremum formula via statistical limit.