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In this article, we introduce an iterative algorithm for finding a common element of the set of common fixed points of a finite family of closed generalized quasi-φ-asymptotically nonexpansive mappings and the set of solutions of equilibrium problem in Banach spaces. Then we study the strong convergence of the algorithm. Our results improve and extend the corresponding results announced by many others. © 2012 Zhao and He; licensee Springer.

fixed point theory and applications

A hybrid iteration scheme for equilibrium problems and common fixed point problems of generalized quasi-ϕ-asymptotically nonexpansive mappings in Banach spaces