Common fixed points for pointwise Lipschitzian semigroups in modular function spaces

Buthinah A. Bin Dehaish, Mohamed A. Khamsi, Wojciech M. Kozlowski

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4 Scopus citations

Abstract

Let C be a ρ-bounded, ρ-closed, convex subset of a modular function space Lρ. We investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups of nonlinear mappings T t : C → C, i.e. a family such that T0(f) = f, T s+t (f) = Ts o Tt(f) and ρ(T(f) - T(g)) ≤ αt (f)α(f - g), where lim sup t→∞αt (f) ≤ 1 for every f ∈ C. In particular, we prove that if Lρ is uniformly convex, then the common fixed point is nonempty ρ-closed and convex.

Original languageBritish English
Article number214
JournalFixed Point Theory and Applications
Volume2013
DOIs
StatePublished - Aug 2013

Keywords

  • Fixed point
  • Modular function space
  • Nonexpansive mapping
  • Orlicz space
  • Pointwise Lipschitzian mapping
  • Pointwise nonexpansive mapping
  • Semigroup
  • Uniform convexity

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