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On modular firmly nonexpansive mappings in the variable exponent sequence spaces \(\ell _{p(\cdot )}\)

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Abstract

In this paper, we reexamine the concept of firmly nonexpansiveness in the modular sense in the variable exponent sequence spaces \(\ell _{p(\cdot )}\). In particular, we extend the classical fixed point results for firmly nonexpansive mappings defined in Banach spaces to the modular case within the spaces \(\ell _{p(\cdot )}\).

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Acknowledgements

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. D-436-363-1441. The authors, therefore, gratefully acknowledge DSR technical and financial support.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Afrah A. N. Abdou

  2. Department of Mathematics, Faculty of Sciences, University of Jeddah, Jeddah, Saudi Arabia

    Afrah A. N. Abdou

  3. Department of Applied Mathematics and Sciences, Khalifa University, Abu Dhabi, United Arab Emirates

    M. A. Khamsi

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  1. Afrah A. N. Abdou
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  2. M. A. Khamsi
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Correspondence to M. A. Khamsi.

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Abdou, A.A.N., Khamsi, M.A. On modular firmly nonexpansive mappings in the variable exponent sequence spaces \(\ell _{p(\cdot )}\). J. Fixed Point Theory Appl. 23, 8 (2021). https://doi.org/10.1007/s11784-020-00842-0

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