, Volume 154, Issue 1, pp 303-320
Date: 11 Feb 2012

Strong Convergence Theorems for Nonexpansive Mappings and Ky Fan Inequalities

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We introduce a new iteration method and prove strong convergence theorems 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 sequences generated by this method converge strongly to the common element in a real Hilbert space. Some preliminary computational experiences are reported.