Asymptotically regular mappings in modular function spaces
Asymptotically regular mappings in modular function spaces
Let ρ be a modular function satisfying a ∆2-type condition and Lρ the corresponding modular space. The main result in this paper states that if C is a ρ-bounded and ρ-a.e sequentially compact subset of Lρ and T : C → C is an asymptotically regular mapping such that lim inf n→∞ [Tn] < 2, where |S| denotes the Lipschitz constant of S, then T has a fixed point. We show that the estimate lim inf n→∞ [Tn] < 2 cannot be, in general, improved.
Plan Andaluz de Investigación (Junta de Andalucía)
- University of Seville Spain
Modular spaces, Modular functions, Fixed point, asymptotically regular mapping, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Fixed-point theorems, modular function, fixed point, \(\Delta_2\)-type condition, Asymptotically regular mappings, modular space, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., Opial property
Modular spaces, Modular functions, Fixed point, asymptotically regular mapping, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Fixed-point theorems, modular function, fixed point, \(\Delta_2\)-type condition, Asymptotically regular mappings, modular space, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., Opial property
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