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Ishikawa type mean convergence theorems for finding common fixed points of nonlinear mappings in Hilbert spaces

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Abstract

Combining the ideas of Ishikawa iteration and mean iteration, we establish weak convergence theorems for finding common fixed points of nonlinear mappings. The mappings are not necessarily continuous or commutative. We consider a class of mappings which includes nonexpansive mappings, generalized hybrid mappings and normally 2-generalized hybrid mappings as special cases. Our result generates many alternative iteration schemes to approximate common fixed points of nonlinear mappings and improves many existing theorems in the literature.

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Acknowledgements

This study is partially supported by the Ryousui Gakujutsu Foundation of Shiga University. The author would really appreciate the anonymous reviewers for their careful reading, 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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Kondo, A. Ishikawa type mean convergence theorems for finding common fixed points of nonlinear mappings in Hilbert spaces. Rend. Circ. Mat. Palermo, II. Ser 72, 1417–1435 (2023). https://doi.org/10.1007/s12215-022-00742-x

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