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Fixed point theorems on generalized \(\alpha\)-nonexpansive multivalued mappings

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Abstract

In this paper, a new class of nonexpansive multivalued mappings, namely, generalized \(\alpha\)-nonexpansive multivalued mappings are introduced. Some topological properties of the fixed point sets of such mappings are derived. Existence results for common fixed points of a pair of single-valued and multivalued mappings both satisfying the generalized \(\alpha\)-nonexpansiveness are proved. Also, weak and strong convergence results of some iterative methods are studied in a uniformly convex Banach space for approximating common fixed points of a pair of single-valued and multivalued mappings as well as two multivalued mappings satisfying the generalized \(\alpha\)-nonexpansiveness.

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Acknowledgements

The authors are thankful to the reviewers for their comments and suggestions to revise the paper into its present form.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    R. Sadhu & C. Nahak

  2. Department of Mathematics, Sreegopal Banerjee College, Magra, 712148, India

    R. Sadhu

  3. Department of Mathematics, Motilal Nehru National Institute of Technology, Prayagraj, Allahabad, 211004, India

    P. Majee

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  1. R. Sadhu
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  2. P. Majee
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  3. C. Nahak
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Correspondence to R. Sadhu.

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Author R. Sadhu declares that he has no conflict of interest. Author P. Majee declares that he has no conflict of interest. Author C. Nahak declares that he has no conflict of interest.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by Samy Ponnusamy.

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Sadhu, R., Majee, P. & Nahak, C. Fixed point theorems on generalized \(\alpha\)-nonexpansive multivalued mappings. J Anal 29, 1165–1190 (2021). https://doi.org/10.1007/s41478-021-00303-y

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  • DOI: https://doi.org/10.1007/s41478-021-00303-y

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