Asymptotically Nonexpansive Mappings in Modular Function Spaces |
| |
| Authors: | T Dominguez-Benavides MA KhamsiS Samadi |
| |
| Institution: | a Department of Mathematical Analysis, University of Seville, P.O. Box 1160, 41080, Seville, Spainb Department of Mathematical Science, The University of Texas at El Paso, El Paso, Texas, 79968, f1mohamed@math.utep.eduf1 |
| |
| 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. |
| |
| Keywords: | asymptotically nonexpansive mappings fixed point modular functions |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
