Strong Convergence Theorems for Nonexpansive Mappings and Ky Fan Inequalities
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- Anh, P.N. J Optim Theory Appl (2012) 154: 303. doi:10.1007/s10957-012-0005-x
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.