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Existence and approximation of fixed points of multivalued generalized α-nonexpansive mappings in Banach spaces

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Abstract

We introduce multivalued generalized α-nonexpansive mappings and present a fixed point result. The multivalued version of the iteration process (Piri et al., Numerical Algorithms, 1–20, 2018) is proposed and some weak and strong convergence results in uniformly convex Banach space are established. Further, we also study the stability of the modified iteration process. Finally, we compare the rate of convergence of suggested multivalued version of iteration process with several known iteration processes through a numerical example.

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Acknowledgments

The authors are grateful to the referees for their valuable comments and suggestions which helped us in improving the presentation of the paper.

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Authors and Affiliations

  1. Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, Lahore, Pakistan

    Hira Iqbal & S. M. Husnine

  2. Department of Mathematics, Government College University, Lahore, 54000, Pakistan

    Mujahid Abbas

  3. Department of Medical Research, China Medical University, No.91, Hsueh-Shih Road, Taichung, Taiwan

    Mujahid Abbas

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  1. Hira Iqbal
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  2. Mujahid Abbas
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  3. S. M. Husnine
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Correspondence to Hira Iqbal.

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Iqbal, H., Abbas, M. & Husnine, S.M. Existence and approximation of fixed points of multivalued generalized α-nonexpansive mappings in Banach spaces. Numer Algor 85, 1029–1049 (2020). https://doi.org/10.1007/s11075-019-00854-z

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