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We discuss determination of jumps for functions with generalized bounded variation. The questions are motivated by A. Set T := [−π, π). Let L(T) denote the set of all periodic and integrable functions with period 2π. For any f ∈ L(T) denote by (1.1) S[f ](x) := a 0 2 + ∞ k=1 A k (x) = a 0 2 + ∞ k=1 (a k cos kx + b k sin kx) and (1.2) S[f ](x) := ∞ k=1 A k(More)
In this paper, we investigate the global attractivity of negative solutions of the nonlinear difference equation x n+1 = 1 − x n−k where A ∈ (−∞, 0), k is a positive integer and initial conditions x −k , · · · , x 0 are arbitrary real numbers. We show that the unique negative equilibrium of above-mentioned equation is a global attractor with a basin under(More)
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