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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.

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This work was supported by National Foundation for Science and Technology Development of Vietnam (NAFOSTED).

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Correspondence to P. N. Anh.

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Anh, P.N. Strong Convergence Theorems for Nonexpansive Mappings and Ky Fan Inequalities. J Optim Theory Appl 154, 303–320 (2012). https://doi.org/10.1007/s10957-012-0005-x

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  • Nonexpansive mapping
  • Fixed point
  • Monotone
  • Lipschitz-type continuous
  • Ky Fan inequality