On the convergence of iteration processes for semigroups of nonlinear mappings in modular function spaces

Authors

Mohamed A. Khamsi, University of Texas at El Paso
Buthinah A. Bin Dehaish, King Abdulaziz University
Wojciech M. Kozlowski, University of New South Wales

Publication Date

2015

Document Type

Article

Comments

Bin Dehaish, B.A., Khamsi, M.A. & Kozlowski, W.M. Fixed Point Theory Appl (2015) 2015: 3. https://doi.org/10.1186/1687-1812-2015-3

Abstract

Let C be a ρ-bounded, ρ-closed, convex subset of a modular function space Lρ. We investigate the problem of constructing common fixed points for asymptotic pointwise nonexpansive semigroups of mappings Tt : C → C, i.e. a family such that T0(f) = f, Ts+t(f) = Ts ◦ Tt(f), and ρ(T(f) – T(g)) ≤ αt(f)ρ(f – g), where lim supt→∞ αt(f) ≤ 1, for every f ∈ C.