Strong convergence of a hybrid iteration scheme for equilibrium problems,variational inequality problems and common fixed point problems,of quasi-φ-asymptotically nonexpansive mappings in banach spaces

We introduce an iterative algorithm for finding a common element of the set of common fixed points of a finite family of closed quasi-φ-asymptotically nonexpansive mappings,the set of solutions of an equilibrium problem,and the set of solutions of the variational inequality problem for a γ-inverse strongly monotone mapping in banach spaces. then we study the strong convergence of the algorithm. our results improve and extend the corresponding results announced by many others. copyright © 2012 jing zhao.