Strong convergence theorems for variational inequality problems and quasi-<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\phi}$$</EquationSource> </InlineEquation>-asymptotically nonexpansive mappings

In this paper, we introduce an iterative process which converges strongly to a common solution of finite family of variational inequality problems for γ-inverse strongly monotone mappings and fixed point of two continuous quasi-<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${\phi}$$</EquationSource> </InlineEquation>-asymptotically nonexpansive mappings in Banach spaces. Our theorems extend and unify most of the results that have been proved for the class of monotone mappings. Copyright Springer Science+Business Media, LLC. 2012