Abstract
Asymptotic properties of solutions to difference equations of the form
Using a new version of the Krasnoselski fixed point theorem and the iterated remainder operator, we establish sufficient conditions under which a given solution of the equation
is an approximative solution to the above equation. Our approach, based on the iterated remainder operator, allows us to control the degree of approximation. We use \(\mathrm {o}(n^s)\), for a given nonpositive real s, as a measure of approximation.
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Migda, J. (2018). Approximative Solutions to Autonomous Difference Equations of Neutral Type. In: Pinelas, S., Caraballo, T., Kloeden, P., Graef, J. (eds) Differential and Difference Equations with Applications. ICDDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 230. Springer, Cham. https://doi.org/10.1007/978-3-319-75647-9_26
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DOI: https://doi.org/10.1007/978-3-319-75647-9_26
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