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.
Highlights
Modular function spaces (MFS) find their roots in the study of the classical function spaces L p (Ω)and their extensions by Orlicz and others
Another interesting use of the modular structure, for whoever is looking for more applications, is the excellent book by Diening et al [2] about Lebesgue and Sobolev spaces with variable exponents
We investigate the case of monotone mappings
Summary
Modular function spaces (MFS) find their roots in the study of the classical function spaces L p (Ω)and their extensions by Orlicz and others. (3) A subset C of Lρ is said to be ρ-closed if for any sequence { gn } in C ρ-convergent to g implies that g ∈ C. Let { f n } ⊂ K be a monotone increasing sequence.
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