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Convergence theorems for a new iteration scheme for mixed-type asymptotically nonexpansive mappings

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Abstract

In this paper, we introduce a new iteration scheme of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings, and prove some weak and strong convergence theorems of the proposed iteration scheme in uniformly convex Banach spaces. Our results improve and extend the corresponding results given by some authors.

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Acknowledgements

The author is extremely grateful to Professor Simeon Reich and the anonymous referee for their valuable comments and useful suggestions which improve the presentation of this paper. The author is grateful to University of Phayao for supporting research project RD60062.

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Correspondence to Tanakit Thianwan.

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Thianwan, T. Convergence theorems for a new iteration scheme for mixed-type asymptotically nonexpansive mappings. J. Fixed Point Theory Appl. 20, 145 (2018). https://doi.org/10.1007/s11784-018-0625-3

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  • DOI: https://doi.org/10.1007/s11784-018-0625-3

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