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1
Content available remote

Measures of noncompactness and normal structure in Banach spaces

100%
García-Falset J., Jiménez-Melado A., Lloréns-Fuster E.
Studia Mathematica
|
1994
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tom 110
|
nr 1
1-8
EN
Sufficient conditions for normal structure of a Banach space are given. One of them implies reflexivity for Banach spaces with an unconditional basis, and also for Banach lattices.
2
Content available remote

Weak uniform normal structure in direct sum spaces

100%
Domínguez Benavides T.
Studia Mathematica
|
1992
|
tom 103
|
nr 3
283-290
EN
The weak normal structure coefficient WCS(X) is computed or bounded when X is a finite or infinite direct sum of reflexive Banach spaces with a monotone norm.
3

Random fixed points for a certain class of asymptotically regular mappings

88%
Thakur B., Jung J., Sahu D., Cho Y.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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1998
|
tom 18
|
nr 1-2
27-43
EN
Let (Ω, σ) be a measurable space and K a nonempty bounded closed convex separable subset of a p-uniformly convex Banach space E for p > 1. We prove a random fixed point theorem for a class of mappings T:Ω×K ∪ K satisfying the condition: For each x, y ∈ K, ω ∈ Ω and integer n ≥ 1, ⃦Tⁿ(ω,x) - Tⁿ(ω,y) ⃦ ≤ aₙ(ω)· ⃦x - y ⃦ + bₙ(ω){ ⃦x -Tⁿ(ω,x) ⃦ + ⃦y - Tⁿ(ω,y) ⃦} + cₙ(ω){ ⃦x - Tⁿ(ω,y) ⃦ + ⃦y - Tⁿ(ω,x) ⃦}, where aₙ, bₙ, cₙ: Ω → [0, ∞) are functions satisfying certain conditions and Tⁿ(ω,x) is the value at x of the n-th iterate of the mapping T(ω,·). Further we establish some random fixed point theorems for these mappings in Hilbert spaces, in $L^p$ spaces, in Hardy spaces $H^p$ and in Sobolev spaces $H^{k,p}$ for 1 < p < ∞ and k ≥ 0. As a consequence of our main result, we extend and randomize the corresponding deterministic ones of Górnicki [14, 15] and others.
4
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A modulus for property (β) of Rolewicz

88%
Ayerbe J. M., Domínguez Benavides T., Francisco Cutillas S.
Colloquium Mathematicum
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1997
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tom 73
|
nr 2
183-191
EN
We define a modulus for the property (β) of Rolewicz and study some useful properties in fixed point theory for nonexpansive mappings. Moreover, we calculate this modulus in $l^p$ spaces for the main measures of noncompactness.
5
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The generalized Day norm. Part I. Properties

75%
Budzyńska M., Grzesik A., Kot M.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2017
|
tom 71
|
nr 2
EN
In this paper we introduce a modification of the Day norm in \(c_0(\Gamma)\) and investigate properties  of this norm.
6
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A new convexity property that implies a fixed point property for $L_{1}$

63%
Lennard C.
Studia Mathematica
|
1991
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tom 100
|
nr 2
95-108
EN
In this paper we prove a new convexity property for L₁ that resembles uniform convexity. We then develop a general theory that leads from the convexity property through normal structure to a fixed point property, via a theorem of Kirk. Applying this theory to L₁, we get the following type of normal structure: any convex subset of L₁ of positive diameter that is compact for the topology of convergence locally in measure, must have a radius that is smaller than its diameter. Indeed, a stronger result holds. The Chebyshev centre of any norm bounded, convergence locally in measure compact subset of L₁ must be norm compact. Immediately from normal structure, we get a new proof of a fixed point theorem for L₁ due to Lami Dozo and Turpin.
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