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Strong Convergence Theorems for Nonexpansive Mappings and Ky Fan Inequalities

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  • P. N. Anh

    (Posts and Telecommunications Institute of Technology)

Abstract

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.

Suggested Citation

  • P. N. Anh, 2012. "Strong Convergence Theorems for Nonexpansive Mappings and Ky Fan Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 303-320, July.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:1:d:10.1007_s10957-012-0005-x
    DOI: 10.1007/s10957-012-0005-x
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    References listed on IDEAS

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    1. A. Tada & W. Takahashi, 2007. "Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 359-370, June.
    2. L. C. Ceng & S. Schaible & J. C. Yao, 2008. "Implicit Iteration Scheme with Perturbed Mapping for Equilibrium Problems and Fixed Point Problems of Finitely Many Nonexpansive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 403-418, November.
    3. Tran Quoc & Pham Anh & Le Muu, 2012. "Dual extragradient algorithms extended to equilibrium problems," Journal of Global Optimization, Springer, vol. 52(1), pages 139-159, January.
    4. Lu-Chuan Ceng & Nicolas Hadjisavvas & Ngai-Ching Wong, 2010. "Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems," Journal of Global Optimization, Springer, vol. 46(4), pages 635-646, April.
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    Cited by:

    1. P. Anh & T. Hai & P. Tuan, 2016. "On ergodic algorithms for equilibrium problems," Journal of Global Optimization, Springer, vol. 64(1), pages 179-195, January.

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