Random fixed points for a certain class of asymptotically regular mappings

• Autorzy: Balwant Singh Thakur , Jong Soo Jung , Daya Ram Sahu , Yeol Je Cho
• Języki publikacji: 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.

Słowa kluczowe

EN

p-uniformly convex Banach space; normal structure; asymptotic center; random fixed point; generalized random Lipschitzian mapping

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 47H10: Fixed-point theorems
• 60H25: Random operators and equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1998
• Tom: 18
• Numer: 1-2
• Strony: 27-43

Daty

wydano

1998

otrzymano

1998-04-15

Twórcy

autor

Balwant Singh Thakur

• Govt. B. H. S. S. Gariaband, Dist. Raipur (M. P.) 493889, India

autor

Jong Soo Jung

• Department of Mathematics, Dong-A University, Pusan 607-714, Korea

autor

Daya Ram Sahu

• Govt. H.S. Kumhari, Dist. Durg. (M. P.) 490042, India

autor

Yeol Je Cho

• Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea

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