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Journal of Applied Mathematics
Volume 2014, Article ID 280158, 8 pages
Research Article

Convergence Theorems for Hierarchical Fixed Point Problems and Variational Inequalities

1Department of Mathematics, Faculty of Science, Erzurum Technical University, 25240 Erzurum, Turkey
2Department of Mathematics, Faculty of Science, Ataturk University, 25240 Erzurum, Turkey

Received 17 March 2014; Accepted 16 June 2014; Published 6 July 2014

Academic Editor: Luigi Muglia

Copyright © 2014 Ibrahim Karahan and Murat Ozdemir. 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.


This paper deals with a modified iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under certain approximate assumptions of mappings and parameters. As a special case, this projection method solves some quadratic minimization problem. It should be noted that the proposed method can be regarded as a generalized version of Wang and Xu (2013), Ceng et al. (2011), Sahu et al. (2012), and many other authors.