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Iterative approximation of fixed points of a general class of non-expansive mappings in hyperbolic metric spaces

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Abstract

In this article, we enquire for a couple of weak and strong convergence results involving generalized \(\alpha \)-Reich-Suzuki non-expansive mappings in the setting of a hyperbolic metric space. Particularly, we make use of the recently proposed JF-iteration scheme to attain our theories and further, we attest that this algorithm has a faster convergence rate than that of \(M^*\) iteration. Additionally, we explore several interesting properties related to the fixed point set of such mappings and approximate fixed point sequences also. Eventually, we furnish pertinent examples to substantiate our attained findings and compare the newly proposed scheme with that of some other well-known algorithms using MATLAB 2017a software.

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Acknowledgements

We are very much thankful to the reviewer for his/her constructive comments and suggestions which have been useful for the improvement of this paper.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Durgapur, Durgapur, India

    Ashis Bera & Lakshmi Kanta Dey

  2. Department of Mathematics, Vellore Institute of Technology, Vellore, India

    Ankush Chanda

  3. Department of Mathematics, Aligarh Muslim University, Aligarh, India

    Javid Ali

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  1. Ashis Bera
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Bera, A., Chanda, A., Dey, L.K. et al. Iterative approximation of fixed points of a general class of non-expansive mappings in hyperbolic metric spaces. J. Appl. Math. Comput. 68, 1817–1839 (2022). https://doi.org/10.1007/s12190-021-01592-z

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