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(phi(n)) (X-n) + (1 - t(n))X-n,
for n is an element of N, when T is a monotone asymptotically nonexpansive self-mapping.