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1998 | 18 | 1-2 | 27-43
Tytuł artykułu

Random fixed points for a certain class of asymptotically regular mappings

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EN
Abstrakty
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.
Twórcy
  • Govt. B. H. S. S. Gariaband, Dist. Raipur (M. P.) 493889, India
  • Department of Mathematics, Dong-A University, Pusan 607-714, Korea
  • Govt. H.S. Kumhari, Dist. Durg. (M. P.) 490042, India
autor
  • Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea
Bibliografia
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Typ dokumentu
Bibliografia
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