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http://hdl.handle.net/20.500.12128/12800| Tytuł: | Stability of functional equations connected with quadrature rules |
| Autor: | Szostok, Tomasz |
| Słowa kluczowe: | stability of functional equations; functional equations stemming from numerical integration |
| Data wydania: | 2016 |
| Źródło: | Aequationes mathematicae, Vol. 90, no. 1 (2016), s 163-172 |
| Abstrakt: | We study the stability properties of the equation F(y)−F(x)=(y−x)∑i=1naif(αix+βiy) which is motivated by numerical integration. In Szostok and Wa̧sowicz (Appl Math Lett 24(4):541–544, 2011) the stability of the simplest equation of the type (0.1) was investigated thus the inequality |F(y)−F(x)−(y−x)f(x+y)|≤ε was studied. In the current paper we present a somewhat different approach to the problem of stability of (0.1). Namely, we deal with the inequality ∣∣∣F(y)−F(x)y−x−∑i=1naif(αix+βiy)∣∣∣≤ε. |
| URI: | http://hdl.handle.net/20.500.12128/12800 |
| DOI: | 10.1007/s00010-016-0415-1 |
| ISSN: | 0001-9054 1420-8903 |
| Pojawia się w kolekcji: | Artykuły (WNŚiT) |
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