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http://dx.doi.org/10.7858/eamj.2012.28.3.265

STRONG CONVERGENCE THEOREMS FOR GENERALIZED VARIATIONAL INEQUALITIES AND RELATIVELY WEAK NONEXPANSIVE MAPPINGS IN BANACH SPACES  

Liu, Ying (College of Mathematics and Computer, Hebei University)
Publication Information
Abstract
In this paper, we introduce an iterative sequence by using a hybrid generalized $f$-projection algorithm for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping an the set of solutions of a generalized variational inequality in a Banach space. Our results extend and improve the recent ones announced by Y. Liu [Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings, J. Glob. Optim. 46 (2010), 319-329], J. Fan, X. Liu and J. Li [Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces, Nonlinear Analysis 70 (2009), 3997-4007], and many others.
Keywords
Generalized variational inequalities; relatively weak nonexpansive mappings; generalized f-projection; Cauchy sequences; continuity;
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