Asymptotically nonexpansive mappings in modular function spaces

T. Dominguez-Benavides, M. A. Khamsi, S. Samadi

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

In this paper, we prove that if ρ is a convex, σ-finite modular function satisfying a Δ2-type condition, C a convex, ρ-bounded, ρ-a.e. compact subset of Lρ, and T: C → C a ρ-asymptotically nonexpansive mapping, then T has a fixed point. In particular, any asymptotically nonexpansive self-map defined on a convex subset of L1(Ω, μ;) which is compact for the topology of local convergence in measure has a fixed point.

Original languageBritish English
Pages (from-to)249-263
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume265
Issue number2
DOIs
StatePublished - 15 Jan 2002

Keywords

  • Asymptotically nonexpansive mappings
  • Fixed point
  • Modular functions

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