Dehaish, B.A.B.; Khamsi, M.A. Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces. Symmetry2018, 10, 481.
Dehaish, B.A.B.; Khamsi, M.A. Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces. Symmetry 2018, 10, 481.
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 defined by $$x_{n+1} = t_n T^{\phi(n)}(x_n) + (1-t_n)x_n,$$ for $n \in \mathbb{N}$, when $T$ is a monotone asymptotically nonexpansive self-mapping.
Keywords
Asymptotically nonexpansive mapping, Fibonacci sequence, fixed point, Mann iteration process, modular function spaces, monotone Lipschitzian mapping, Opial condition, uniformly convexity.
Subject
MATHEMATICS & COMPUTER SCIENCE, Analysis
Copyright:
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