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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 589282, 11 pages
Research Article

An Iterative Shrinking Metric -Projection Method for Finding a Common Fixed Point of a Closed and Quasi-Strict -Pseudocontraction and a Countable Family of Firmly Nonexpansive Mappings and Applications in Hilbert Spaces

1Department of Mathematics, Faculty of Science, Naresuan University, 99 Moo 9, Phitsanulok-Nakhon Sawan Road, Tha Pho, Mueang, Phitsanulok 65000, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 29 August 2013; Accepted 18 October 2013

Academic Editor: Shawn X. Wang

Copyright © 2013 Kasamsuk Ungchittrakool and Duangkamon Kumtaeng. 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 create some new ideas of mappings called quasi-strict -pseudocontractions. Moreover, we also find the significant inequality related to such mappings and firmly nonexpansive mappings within the framework of Hilbert spaces. By using the ideas of metric -projection, we propose an iterative shrinking metric -projection method for finding a common fixed point of a quasi-strict -pseudocontraction and a countable family of firmly nonexpansive mappings. In addition, we provide some applications of the main theorem to find a common solution of fixed point problems and generalized mixed equilibrium problems as well as other related results.