Strong convergence theorems for a common point of solution of variational inequality, solutions of equilibrium and fixed point problems
1 Department of Mathematics, University of Botswana, Pvt. Bag 00704, Gaborone, Botswana
2 Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Fixed Point Theory and Applications 2012, 2012:119 doi:10.1186/1687-1812-2012-119Published: 23 July 2012
We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for continuous monotone mapping, solution of equilibrium problem and a common fixed point of finite family of asymptotically regular uniformly continuous relatively asymptotically nonexpansive mappings in Banach spaces. Our scheme does not involve computation of Cn+1 from Cn for each n ≥ 1. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
Mathematics Subject Classification (2000): 47H05, 47H09, 47H10, 47J05, 47J25