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Strong convergence theorems with three-step iteration in star-shaped metric spaces

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  • The author considers a Noor-type three-step iterative scheme including Ishikawa-type scheme as a special case to approximate common fixed points of an infinite family of uniformly quasi-Lipschitzian mappings and an infinite family of nonexpansive mappings in star-shaped metric spaces. His results are cases of star-shaped metric space of results shown in [7].
    Mathematics Subject Classification: 47H10, 47H17, 49J40.

    Citation:

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  • [1]

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    Q. Y. Liu, Z. B. Liu and N. J. Huang, Approximating the common fixed points of two sequences of uniformly quasi-Lipschitzian mappings in convex metric spaces, Appl. Math. Comput., 216 (2010), 883-889.doi: 10.1016/j.amc.2010.01.096.

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    M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl., 251 (2000), 217-229.doi: 10.1006/jmaa.2000.7042.

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    M. A. Noor and Z. Huang, Three-step methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput., 187 (2007), 680-685.doi: 10.1016/j.amc.2006.08.088.

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    Y. X. Tian, Convergence of an Ishikawa type iterative scheme for asymptotically quasi-nonexpansive mappings, Comput. Math. Appl., 49 (2005), 1905-1912.doi: 10.1016/j.camwa.2004.05.017.

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    B. Xu and M. A. Noor, Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl., 267 (2002), 444-453.doi: 10.1006/jmaa.2001.7649.

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    Y. Yao and M. A. Noor, Convergence of three-step iteration for asymptotically nonexpansive mappings, Appl. Math. Comput., 187 (2007), 883-892.doi: 10.1016/j.amc.2006.09.008.

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