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