Asymptotically Nonexpansive Mappings in Modular Function Spaces
Copyright policy )Asymptotically Nonexpansive Mappings in Modular Function Spaces
In this paper, we prove that if ρ is a convex, σ-finite modular function satisfying a ∆2-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.
Dirección General de Investigación Científica y Técnica
Plan Andaluz de Investigación (Junta de Andalucía)
- University of Seville Spain
- The University of Texas at El Paso United States
- The University of Texas System United States
- Universidad de Sevilla (US) Spain
asymptotically nonexpansive mappings, Applied Mathematics, Asymptotically nonexpansive mappings, Modular functions, Fixed point, compact convex subset, Fixed-point theorems, topology of local convergence, modular functions, fixed point, modular space, asymptotically nonexpansive, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., Analysis
asymptotically nonexpansive mappings, Applied Mathematics, Asymptotically nonexpansive mappings, Modular functions, Fixed point, compact convex subset, Fixed-point theorems, topology of local convergence, modular functions, fixed point, modular space, asymptotically nonexpansive, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., Analysis
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