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On subadditive functions and ψ-additive mappings

Janusz Matkowski (2003)

Open Mathematics

In [4], assuming among others subadditivity and submultiplicavity of a function ψ: [0, ∞)→[0, ∞), the authors proved a Hyers-Ulam type stability theorem for “ψ-additive” mappings of a normed space into a normed space. In this note we show that the assumed conditions of the function ψ imply that ψ=0 and, consequently, every “ψ-additive” mapping must be additive

On the asymptotic behavior of solutions of linear difference equations.

Jerzy Popenda, Ewa Schmeidel (1994)

Publicacions Matemàtiques

In the paper sufficient conditions for the difference equation :Δxn = Σi=0r an(i) xn+ito have a solution which tends to a constant, are given. Applying these conditions, an asymptotic formula for a solution of an m-th order equation is presented.

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