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Abstract and Applied Analysis
Volume 2012, Article ID 536283, 20 pages
Research Article

An Iterative Shrinking Projection Method for Solving Fixed Point Problems of Closed and 𝜙-Quasi-Strict Pseudocontractions along with Generalized Mixed Equilibrium Problems in Banach Spaces

1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 22 April 2012; Revised 4 July 2012; Accepted 29 July 2012

Academic Editor: Simeon Reich

Copyright © 2012 Kasamsuk Ungchittrakool. 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 provide some new type of mappings associated with pseudocontractions by introducing some actual examples in smooth and strictly convex Banach spaces. Moreover, we also find the significant inequality related to the mappings mentioned in the paper and the mappings defined from generalized mixed equilibrium problems on Banach spaces. We propose an iterative shrinking projection method for finding a common solution of generalized mixed equilibrium problems and fixed point problems of closed and 𝜙-quasi-strict pseudo-contractions. Our results hold in reflexive, strictly convex, and smooth Banach spaces with the property (𝐾). The results of this paper improve and extend the corresponding results of Zhou and Gao (2010) and many others.