Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We investigate the asymptotic behaviour at infinity of solutions of the equation [formula].We show among others that, under some assumptions, any positive solution of the equation which is integrable on a vicinity of infinity or vanishes at +∞ tends on some sequence to zero faster than some exponential function, but it does not vanish faster than another such function.
Czasopismo
Rocznik
Tom
Strony
559--577
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Silesian University, Institute of Mathematics, ul. Bankowa 14, 40-007 Katowice, Poland, sokolowski@ux2.math.us.edu.pl
Bibliografia
- [1] K. Baron, W. Jarczyk, Recent results on functional equations in a single variable, perspectives and open problems, Aequationes Math. 61 (2001), 1–48.
- [2] K. Baron, W. Jarczyk, Random-valued functions and iterative functional equations, Aequationes Math. 67 (2004), 140–153.
- [3] G. Belitskii, V. Tkachenko, One-dimensional functional equations, Operator Theory: Advances and Applications 144, Birkhäuser Verlag, Basel, 2003.
- [4] R.O. Davies, A.J. Ostaszewski, On a difference-delay equation, J. Math. Anal. Appl. 247 (2000), 608–626.
- [5] W. Jarczyk, A recurrent method of solving iterative functional equations, Prace Naukowe Uniwersytetu Sl¸askiego w Katowicach 1206, Uniwersytet Sl¸aski, Katowice, 1991.
- [6] M. Kuczma, Functional equations in a single variable, Monografie Mat. 46, PWN-Polish Scientific Publishers, Warsaw, 1968.
- [7] M. Kuczma, B. Choczewski, R. Ger, Iterative functional equations, Encyclopedia of Mathematics and Its Applications 32, Cambridge University Press, Cambridge, 1990.
- [8] M. Laczkovich, Nonnegative measurable solutions of difference equations, J. London Math. Soc. (2) 34 (1986), 139–147.
- [9] Ka-Sing Lau, Wei-Bin Zeng, The convolution equation of Choquet and Deny on semigroups,Studia Math. 97 (1990), 115–135.
- [10] P.-A. Meyer, Probability and potentials, Blaisdell Publishing Company, Waltham, 1966.
- [11] M. Pycia, A convolution inequality, Aequationes Math. 57 (1999), 185–200.
- [12] B. Ramachandran, Ka-Sing Lau, Functional equations in probability theory, Probability and Mathematical Statistics, Academic Press, Inc., Boston, 1991.
- [13] D. Sokołowski, Solutions with constant sign at infinity of a linear functional equation of infinite order, J. Math. Anal. Appl. 310 (2005), 144–160.
- [14] D. Sokołowski, Exponential behaviour of solutions of a linear functional equation, Aequationes Math. 73 (2007), 291–300.
- [15] D. Sokołowski, Solutions with exponential character to a linear functional equation and roots of its characteristic equation, J. Math. Anal. Appl. 327 (2007), 351–361.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHS-0004-0012