Hybrid methods for accretive variational inequalities involving pseudocontractions in Banach spaces

Abstract

Abstract We use strongly pseudocontractions to regularize a class of accretive variational inequalities in Banach spaces, where the accretive operators are complements of pseudocontractions and the solutions are sought in the set of fixed points of another pseudocontraction. In this paper, we consider an implicit scheme that can be used to find a solution of a class of accretive variational inequalities. Our results improve and generalize some recent results of Yao et al. (Fixed Point Theory Appl, doi:10.1155/2011/180534, 2011) and Lu et al. (Nonlinear Anal, 71(3-4), 1032-1041, 2009). 2000 Mathematics subject classification 47H05; 47H09; 65J15

Keywords

• hybrid method
• accretive operator
• variational inequality
• pseudocontraction