A modified Halpern-type iterative method of a system of equilibrium problems and a fixed point for a totally quasi-φ-asymptotically nonexpansive mapping in a banach space

The purpose of this paper is to introduce the modified halpern-type iterative method by the generalized f-projection operator for finding a common solution of fixed-point problem of a totally quasi-φ-asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth and strictly convex banach space with the kadec-klee property. consequently,we prove the strong convergence for a common solution of above two sets. our result presented in this paper generalize and improve the result of chang et al.,(2012),and some others. copyright © 2012 preedaporn kanjanasamranwong et al.