Approximation of common fixed point of families of nonlinear mappings with applications

It is our purpose in this paper to show that some results obtained in uniformly convex real Banach space with uniformly Gâteaux differentiable norm are extendable to more general reflexive and strictly convex real Banach space with uniformly Gâteaux differentiable norm. Demicompactness condition imposed in such results is dispensed with. Furthermore, Applications of our theorems to approximation of common fixed point of countable infinite family of continuous pseudocontractive mappings and approximation of common solution of countable infinite family of generalized mixed equilibrium problems are also discussed. Our theorems improve, generalize, unify and extend several recently announced results.