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The Fibonacci–Mann iteration for monotone asymptotically pointwise nonexpansive mappings

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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.

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  1. Department of Mathematics, Faculty of Science University of Jeddah, Jeddah, 21589, Saudi Arabia

    Buthinah A. Bin Dehaish

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  1. Buthinah A. Bin Dehaish
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Correspondence to Buthinah A. Bin Dehaish.

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Bin Dehaish, B.A. The Fibonacci–Mann iteration for monotone asymptotically pointwise nonexpansive mappings. J. Fixed Point Theory Appl. 21, 17 (2019). https://doi.org/10.1007/s11784-018-0643-1

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