Approximation methods of a common fixed point of nonexpansive mappings in a Hilbert space

This thesis is concerned with convergence for finding a common fixed point of two nonexpansive mappings on a Hilbert space. We introduce a new general iterative scheme modified by Mann’s iteration of Cesarp means. We present weak and strong convergence of this scheme for finding a common fixed point of these mappings which extend Wang. And then, we also establish strong convergence theorems of the scheme modify by using viscosity iterative scheme to solve the variational inequality problem over the common fixed point of theses mappings which generalize many known results such as Jankaew, et al.; Markshoe and Wangkeeree.