Strong convergence theorems obtained by a generalized projections hybrid method for families of mappings in Banach spaces

Let CC be a nonempty, closed and convex subset of a uniformly convex and smooth Banach space and let {Tn}{Tn} be a family of mappings of CC into itself such that the set of all common fixed points of {Tn}{Tn} is nonempty. We consider a sequence {xn}{xn} generated by the hybrid method by generalized projection in mathematical programming. We give conditions on {Tn}{Tn} under which {xn}{xn} converges strongly to a common fixed point of {Tn}{Tn} and generalize the results given in [12], [14], [13] and [11].