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Existence and convergence theorems concerning common fixed points of nonlinear semigroups of weak contractions

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Abstract

Nowadays, the usage of the existence and convergence results of a common fixed point for nonlinear semigroups of various kinds of self-mappings is applied to several problems in mathematics and another branches. Surprisingly, nobody considered the study on the nonlinear semigroups of weak contraction self-mappings in the sense of Berinde. The purpose of this paper is to attempt to complete this direction and so we investigate the existence of the common fixed point for nonlinear semigroups of weak contraction self-mappings in the sense of Berinde on a bounded closed convex subset of a real Banach space with uniformly normal structure. More precisely, we prove the convergence theorem for the common fixed point of a weak contraction semigroups. An illustrative example is presented.

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Acknowledgements

This study was supported by Thammasat University Research Fund, Contract No. FT 009/2563.

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  1. Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani, 12120, Thailand

    Thitima Kesahorm & Wutiphol Sintunavarat

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  1. Thitima Kesahorm
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  2. Wutiphol Sintunavarat
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Correspondence to Wutiphol Sintunavarat.

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Kesahorm, T., Sintunavarat, W. Existence and convergence theorems concerning common fixed points of nonlinear semigroups of weak contractions. J. Fixed Point Theory Appl. 22, 70 (2020). https://doi.org/10.1007/s11784-020-00805-5

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  • DOI: https://doi.org/10.1007/s11784-020-00805-5

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