Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces
Buthinah Abdullatif Bin Dehaish, Mohamed A. Khamsi · Symmetry · 2018
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.