The convex feasibility problem (CFP) of finding a point in the nonempty intersection is considered, where is an integer and the 's are assumed to be convex closed subsets of a Banach space . By using hybrid iterative methods, we prove theorems on the strong convergence to a common fixed point for a finite family of relatively nonexpansive mappings. Then, we apply our results for solving convex feasibility problems in Banach spaces.

We introduce an iterative sequence and prove a weak convergence theorem for finding a solution of a system of mixed equilibrium problems and the set of fixed points of a quasi-nonexpansive mapping in Hilbert spaces. Moreover, we apply our result to obtain a weak convergence theorem for finding a solution of a system of mixed equilibrium problems and the set of fixed points of a nonspreading mapping. The result obtained in this paper improves and extends the recent ones announced by Moudafi (2009),Iemoto and Takahashi (2009), and many others. Using this result, we improve and unify several results in fixed point problems and equilibrium problems.