Approximating a common fixed point of a finite family of nonlinear mappings in modular function spaces

Abstract

In this study, it is our purpose to investigate an algorithm for approximating a common fixed point of a finite family of \(\rho \)-quasi-nonexpansive mappings. In addition, we propose and analyze a scheme which estimates a common fixed point of a finite family of multivalued mappings in modular function spaces. As a consequence, we establish the \(\rho \)-convergence of the proposed algorithms under some mild conditions. In addition, some numerical examples which support our main results are presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

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Acknowledgements

The authors wish to thank the referees for their valuable comments on an earlier version of this paper. The first author is supported by Simons Foundation based at Botswana international University of Science and Technology (BIUST), Palapye, Botswana. He would like to thank the Foundation for the financial support.

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All authors contributed equally to this work. All authors read and approved the final manuscript.

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Correspondence to Habtu Zegeye.

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Communicated by Jose Alberto Cuminato.

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Wega, G.B., Zegeye, H. Approximating a common fixed point of a finite family of nonlinear mappings in modular function spaces. Comp. Appl. Math. 38, 99 (2019). https://doi.org/10.1007/s40314-019-0863-z

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Keywords

  • Fixed points
  • Modular function space
  • \(\rho \)-Quasi-nonexpansive
  • \(\rho \)-Convergence

Mathematics Subject Classification

  • 46B20
  • 46E30
  • 47H09
  • 47H10