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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) uniformly in a neighborhood of the origin, where m > 1, ; (c) . Let x₀,x₁ ∈ (0,α) and , n ∈ ℕ. Then the sequence (xₙ) satisfies the following asymptotic formula:
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We characterize the boundedness and compactness of composition operators from weighted Bergman-Privalov spaces to Zygmund type spaces on the unit disk.
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