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The Fibonacci–Mann iteration for monotone asymptotically pointwise nonexpansive mappings

  • Buthinah A. Bin DehaishEmail author
Article
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Abstract

In this work, we investigate the convergence of the Fibonacci–Mann iteration associated with a monotone asymptotic pointwise nonexpansive mapping defined in a modular function space. The first main result deals with the modular convergence of such iteration when the mapping is assumed to be compact. Relaxing the compactness assumption, we obtain a \(\rho \)-a.e. convergence of the iteration. These two results are similar to the main conclusions of the original work of Schu.

Keywords

Asymptotically pointwise nonexpansive mapping fibonacci sequence fixed point Mann iteration process modular function spaces monotone Lipschitzian mapping uniform convexity 

Mathematics Subject Classification

Primary 46B20 47E10 

Notes

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsFaculty of Science University of JeddahJeddahSaudi Arabia

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