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Approximating common fixed points of a family of non-self mappings in CAT(0) spaces

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Abstract

In this paper, we construct an iterative scheme for approximating common fixed points of a countable family of quasi-nonexpansive non-self mappings in a complete CAT(0) space. In addition, we prove \(\triangle \)-convergence and strong convergence results of the scheme under appropriate conditions. Moreover, we construct an iterative scheme for approximating common fixed points of a countable family of demicontractive mappings and establish strong convergence result of the scheme under some mild conditions. Our results improve and generalize most of the results in the literature.

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Acknowledgements

The authors are grateful to the referees and the editor for their careful observation and valuable comments and suggestions which lead to the present form of the paper.

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Author notes

  1. Abebe Regassa Tufa and Habtu Zegeye contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, University of Botswana, P. Bag 00704, Gaborone, Botswana

    Abebe Regassa Tufa

  2. Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana

    Habtu Zegeye

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  1. Abebe Regassa Tufa
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  2. Habtu Zegeye
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Correspondence to Habtu Zegeye.

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Tufa, A.R., Zegeye, H. Approximating common fixed points of a family of non-self mappings in CAT(0) spaces. Bol. Soc. Mat. Mex. 28, 3 (2022). https://doi.org/10.1007/s40590-021-00394-4

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