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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 806537, 12 pages
http://dx.doi.org/10.1155/2014/806537
Research Article

Some Convergence and Stability Results for the Kirk Multistep and Kirk-SP Fixed Point Iterative Algorithms

1Department of Mathematics, Yildiz Technical University, Davutpasa Campus, Esenler, 34220 Istanbul, Turkey
2Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34210 Istanbul, Turkey
3Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, USA

Received 1 July 2013; Accepted 10 November 2013; Published 3 February 2014

Academic Editor: Micah Osilike

Copyright © 2014 Faik Gürsoy et al. 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

The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related to the stability results for the Kirk multistep and Kirk-SP iterative processes by employing certain contractive-like operators. Our results generalize and unify some other results in the literature.