Strong Convergence Theorems for Nonexpansive Mappings and Ky Fan Inequalities

Abstract

Abstract We introduce a new iteration method and prove strong convergence the- orems for finding a common element of the set of fixed points of a nonexpansive mapping and the solution set of monotone and Lipschitz-type continuous Ky Fan inequality. Under certain conditions on parameters, we show that the iteration se- quences generated by this method converge strongly to the common element in a real Hilbert space. Some preliminary computational experiences are reported.