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Iterative approximation to common best proximity points of proximally mean nonexpansive mappings in Banach spaces

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Abstract

In this paper, we introduce the new class of mappings called proximally mean nonexpansive mappings. Further, we construct the Ishikawa iteration scheme associated with two non-self mappings, and we approximate a common best proximity point for a pair of proximally mean nonexpansive mappings via this Ishikawa iteration. As a consequence of our main result, we approximate a best proximity point for proximal mean nonexpansive mappings. Our new results complement and extend recent related results in the literature.

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Acknowledgements

The authors would like to thank the National Board for Higher Mathematics (NBHM), DAE, Govt. of India for providing a financial support under the grant no. 02011/22/2017/R&D II/14080.

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  1. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, 641112, TN, India

    V. Pragadeeswarar & R. Gopi

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  1. V. Pragadeeswarar
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  2. R. Gopi
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Correspondence to V. Pragadeeswarar.

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Pragadeeswarar, V., Gopi, R. Iterative approximation to common best proximity points of proximally mean nonexpansive mappings in Banach spaces. Afr. Mat. 32, 289–300 (2021). https://doi.org/10.1007/s13370-020-00826-w

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  • DOI: https://doi.org/10.1007/s13370-020-00826-w

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