Preprint Article Version 1 This version is not peer-reviewed

# Fibonacci-Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces

Version 1 : Received: 5 September 2018 / Approved: 7 September 2018 / Online: 7 September 2018 (10:58:24 CEST)

A peer-reviewed article of this Preprint also exists.

Dehaish, B.A.B.; Khamsi, M.A. Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces. Symmetry 2018, 10, 481. Dehaish, B.A.B.; Khamsi, M.A. Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces. Symmetry 2018, 10, 481.

Journal reference: Symmetry 2018, 10, 481
DOI: 10.3390/sym10100481

## 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.

## Subject Areas

Asymptotically nonexpansive mapping, Fibonacci sequence, fixed point, Mann iteration process, modular function spaces, monotone Lipschitzian mapping, Opial condition, uniformly convexity.