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Strong convergence of Mann’s type iteration method for an infinite family of generalized asymptotically nonexpansive nonself mappings in Hilbert spaces

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Abstract

Let \(C\) be a nonempty closed convex subset of a real Hilbert space \(H\). Let \(\{T_i\}^{\infty }_{i=1}:C\rightarrow H\) be an infinite family of generalized asymptotically nonexpansive nonself mappings. By using a specific way of choosing the indexes of the involved mappings, we prove strong convergence of Mann’s type iteration to a common fixed point of \(\{T_i\}^{\infty }_{i=1}\) without the compactness assumption imposed either on \(T\) or on \(C\) provided that the interior of common fixed points is nonempty. The results extend previous results restricted to the situation of at most finite families of such mappings.

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Acknowledgments

The author is greatly grateful to the referees for their useful suggestions by which the contents of this article are improved. This work was supported by the National Natural Science Foundation of China (Grant No.11061037).

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  1. College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, 650221, People’s Republic of China

    Wei-Qi Deng

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  1. Wei-Qi Deng
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Deng, WQ. Strong convergence of Mann’s type iteration method for an infinite family of generalized asymptotically nonexpansive nonself mappings in Hilbert spaces. Optim Lett 8, 533–542 (2014). https://doi.org/10.1007/s11590-012-0595-0

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