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Mean convergence theorems using hybrid methods to find common fixed points for noncommutative nonlinear mappings in Hilbert spaces

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Abstract

This paper considers approximation methods to find common fixed points for two general nonlinear mappings that contain generalized hybrid mappings or normally 2-generalized hybrid mappings. First, we combine Nakajo and Takahashi’s hybrid method with a mean iteration method and prove three strong convergence theorems that approximate common fixed points for nonlinear mappings. We then develop Takahashi, Takeuchi and Kubota’s shrinking projection method and prove three strong convergence theorems. Nonlinear mappings are not necessarily continuous or commutative.

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Acknowledgements

This study is partially supported by the Ryousui Gakujutsu Foundation of Shiga University. The author would like to thank two anonymous referees for their helpful comments and advice.

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  1. Department of Economics, Shiga University, Banba 1-1-1, Hikone, Shiga, 522-0069, Japan

    Atsumasa Kondo

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  1. Atsumasa Kondo
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Correspondence to Atsumasa Kondo.

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Kondo, A. Mean convergence theorems using hybrid methods to find common fixed points for noncommutative nonlinear mappings in Hilbert spaces. J. Appl. Math. Comput. 68, 217–248 (2022). https://doi.org/10.1007/s12190-021-01527-8

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  • DOI: https://doi.org/10.1007/s12190-021-01527-8

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