http://hdl.handle.net/20.500.12128/15959
Tytuł: | On The Solutions of The Equation f(xf(y)k+yf(x)‘)=f(x)f(y) |
Autor: | Sablik, Maciej Urban, Paweł |
Słowa kluczowe: | functional equations; Gołąb-Sohinzel equation |
Data wydania: | 1985 |
Źródło: | Demonstratio Mathematica, Vol. 18, nr 3 (1985) s. 863-867 |
Abstrakt: | The functional equation (1) f(xf(y)k + yf(x)1) « f(x)f(y), where k and 1 are positive integers and the unknown function f maps 1R. into itself, has appeared in connection with determining some subsemigroups of the group Lg (of. [2]). Putting k » 0 and 1 = 1 we get the Gołąb-Sohinzel equation as a particular case of (1) which has been studied by many authors including N. Brillouet who in [l] has also dealt with continuous solutions of equation f(xf(y) +yf(x)) «cxf(x)f(y). Our results presented here generalize those from [4j and [1] (in the oase ot= 1). They are also more general than it was announoed by M. Sablik at the 21st Symposium on Functional Bquations (of. [33) (Fragment tekstu). |
URI: | http://hdl.handle.net/20.500.12128/15959 |
DOI: | 10.1515/dema-1985-0317 |
ISSN: | 2391-4661 0420-1213 |
Pojawia się w kolekcji: | Artykuły (WNŚiT) |
Plik | Opis | Rozmiar | Format | |
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Sablik_On_The_Solutions_of_the_Equation.pdf | 288,7 kB | Adobe PDF | Przejrzyj / Otwórz |
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