Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities
C.E. Chidume, C.O. Chidume, C. O. Chidume, C.O. Chidume, Bashir Ali · Journal of Inequalities and Applications · 2008
Let be a real -uniformly smooth Banach space with constant , . Let and be a nonexpansive map and an -strongly accretive map which is also -Lipschitzian, respectively. Let be a real sequence in that satisfies the following condition: and . For and , define a sequence iteratively in by , , . Then, converges strongly to the unique solution of the variational inequality problem (search for such that for all , where . A convergence theorem related to finite family of nonexpansive maps is also proved.