Approximating a common fixed point of a finite family of nonlinear mappings in modular function spaces
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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.
KeywordsFixed points Modular function space \(\rho \)-Quasi-nonexpansive \(\rho \)-Convergence
Mathematics Subject Classification46B20 46E30 47H09 47H10
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.
All authors contributed equally to this work. All authors read and approved the final manuscript.
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Conflict of interest
The authors declare that they have no competing interests.
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