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Symmetry 2018, 10(10), 481; https://doi.org/10.3390/sym10100481

Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces

1
Department of Mathematics, Faculty of Science For Girls, King Abdulaziz University, Jeddah 21593, Saudi Arabia
2
Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah 23218, Saudi Arabia
3
Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA
4
Department of Mathematics & Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
*
Author to whom correspondence should be addressed.
Received: 5 September 2018 / Revised: 25 September 2018 / Accepted: 8 October 2018 / Published: 11 October 2018
(This article belongs to the Special Issue Fixed Point Theory and Fractional Calculus with Applications)
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Abstract

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci–Mann iteration process, introduced recently by Alfuraidan and Khamsi, defined by x n + 1 = t n T ϕ ( n ) ( x n ) + ( 1 t n ) x n , for n N , when T is a monotone asymptotically nonexpansive self-mapping. View Full-Text
Keywords: asymptotically nonexpansive mapping; Fibonacci sequence; fixed point; Mann iteration process; modular function spaces; monotone Lipschitzian mapping; opial condition; uniformly convexity asymptotically nonexpansive mapping; Fibonacci sequence; fixed point; Mann iteration process; modular function spaces; monotone Lipschitzian mapping; opial condition; uniformly convexity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Bin Dehaish, B.A.; Khamsi, M.A. Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces. Symmetry 2018, 10, 481.

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