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A New S-Type Iteration Scheme for Generalized Nonexpansive Mappings

Proceedings of the National Academy of Sciences, India Section A: Physical Sciences volume 89, pages 149–153 (2019)Cite this article

Abstract

Different iterative processes have been used recently to approximate the fixed points of multivalued nonexpansive mappings. Among these iterative procedures iteration scheme due to Sastry and Babu (Czechoslovak Math J 55:817–826, 2005), Panyanak (Comput Math Appl 54:872–877, 2007), Song and Wang (Nonlinear Anal 70:1547–1556, 2009) and Shahzad and Zegeye (Nonlinear Anal 71:838–844, 2009) are notable generalizations of Mann and Ishikawa iteration process especially in the case of multivalued mappings. A new S-type iteration scheme for a multivalued generalized nonexpansive mapping is introduced here. Some convergence theorems are proved by using the same iteration scheme. In this process, many existing results in literature are extended and improved.

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Acknowledgements

The first author is highly grateful to UGC for providing financial support in form of BSR-Start Up research grant.

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Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, New Delhi, 110025, India

    Izhar Uddin

  2. Department of Mathematics, FET, Manav Rachna International University, Faridabad, Haryana, 121001, India

    Arti Saxena

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  1. Izhar Uddin
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  2. Arti Saxena
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Correspondence to Izhar Uddin.

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Uddin, I., Saxena, A. A New S-Type Iteration Scheme for Generalized Nonexpansive Mappings. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 89, 149–153 (2019). https://doi.org/10.1007/s40010-017-0420-3

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  • DOI: https://doi.org/10.1007/s40010-017-0420-3

Keywords

  • Banach spaces
  • S-iteration
  • Generalized nonexpansive mappings
  • Fixed Point Theorem
  • Condition (C)