TY - JOUR
T1 - Asymptotically nonexpansive mappings in modular function spaces
AU - Dominguez-Benavides, T.
AU - Khamsi, M. A.
AU - Samadi, S.
PY - 2002/1/15
Y1 - 2002/1/15
N2 - 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.
AB - 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.
KW - Asymptotically nonexpansive mappings
KW - Fixed point
KW - Modular functions
UR - http://www.scopus.com/inward/record.url?scp=0037081666&partnerID=8YFLogxK
U2 - 10.1006/jmaa.2000.7275
DO - 10.1006/jmaa.2000.7275
M3 - Article
AN - SCOPUS:0037081666
SN - 0022-247X
VL - 265
SP - 249
EP - 263
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -