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Asymptotic behavior of a sequence defined by iteration with applications

100%

Stević S.

Colloquium Mathematicum

2002

tom 93

nr 2

267-276

We consider the asymptotic behavior of some classes of sequences defined by a recurrent formula. The main result is the following: Let f: (0,∞)² → (0,∞) be a continuous function such that (a) 0 < f(x,y) < px + (1-p)y for some p ∈ (0,1) and for all x,y ∈ (0,α), where α > 0; (b) $f(x,y) = px + (1-p)y - ∑_{s=m}^{∞}𝒦_{s}(x,y)$ uniformly in a neighborhood of the origin, where m > 1, $𝒦_{s}(x,y) = ∑_{i=0}^{s} a_{i,s}x^{s-i}y^{i}$; (c) $𝒦ₘ(1,1) = ∑_{i=0}^{m} a_{i,m} > 0$. Let x₀,x₁ ∈ (0,α) and $x_{n+1} = f(xₙ,x_{n-1})$, n ∈ ℕ. Then the sequence (xₙ) satisfies the following asymptotic formula: $xₙ ∼ ((2-p)/((m-1)∑_{i=0}^{m} a_{i,m}))^{1/(m-1)} 1/{\root{m-1}\of{n}}$.

Composition operators from weighted Bergman-Privalov spaces to Zygmund type spaces on the unit disk

63%

Stević S., Sharma A.

Annales Polonici Mathematici

2012

tom 105

nr 1

77-86

We characterize the boundedness and compactness of composition operators from weighted Bergman-Privalov spaces to Zygmund type spaces on the unit disk.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Colloquium Mathematicum

2 Stević S.

1 Sharma A.

1 2012

1 2002

Wyniki wyszukiwania

Asymptotic behavior of a sequence defined by iteration with applications

Composition operators from weighted Bergman-Privalov spaces to Zygmund type spaces on the unit disk