Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011, Article ID 852789, 22 pages doi: Research Article Iterative Methods for Family of Strictly Pseudocontractive Mappings and System of Generalized Mixed Equilibrium Problems and Variational Inequality Problems Yekini Shehu Mathematics Institute, African University of Science and Technology, Abuja, Nigeria Correspondence should be addressed to Yekini Shehu, deltanougt2006@ Received 6 September 2010; Accepted 25 November 2010 Academic Editor: S. Al-Homidan Copyright q 2011 Yekini Shehu. 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. | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 852789 22 pages doi 2011 852789 Research Article Iterative Methods for Family of Strictly Pseudocontractive Mappings and System of Generalized Mixed Equilibrium Problems and Variational Inequality Problems Yekini Shehu Mathematics Institute African University of Science and Technology Abuja Nigeria Correspondence should be addressed to Yekini Shehu deltanougt2006@ Received 6 September 2010 Accepted 25 November 2010 Academic Editor S. Al-Homidan Copyright 2011 Yekini Shehu. 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 introduce a new iterative scheme by hybrid method for finding a common element of the set of common fixed points of infinite family of fc-strictly pseudocontractive mappings and the set of common solutions to a system of generalized mixed equilibrium problems and the set of solutions to a variational inequality problem in a real Hilbert space. We then prove strong convergence of the scheme to a common element of the three above described sets. We give an application of our results. Our results extend important recent results from the current literature. 1. Introduction Let K be a nonempty closed and convex subset of a real Hilbert space H. A mapping A K H is called monotone if Ax - Ay x - y 0 Nx y e K. A mapping A K H is called inverse-strongly monotone see . 1 2 if there exists a positive real number A such that Ax - Ay x - y A Ax - Ay 2 for all x y e K. For such a case A is called A-inverse-strongly monotone. A A-inverse-strongly monotone is sometime called A-cocoercive. A mapping A is said to be relaxed A-cocoercive if there exists A 0 such that Ax - Ay x - y -AII Ax - Ay 2 Nx y e K. 2 Fixed Point Theory and Applications A is said to be relaxed 1 Yficocoercive if .
