参考文献:1.Batko B.: On approximation of approximate solutions of Dhombres鈥?equation. J. Math. Anal. Appl. 340, 424鈥?32 (2008)View Article MATH MathSciNet 2.Batko B.: Stability of Dhombres鈥?equation. Bull. Aust. Math. Soc. 70, 499鈥?05 (2004)View Article MATH MathSciNet 3.Batko, B.: Stability of the exponential functional equation in Riesz algebras (to appear) 4.Batko B.: The stability of Dhombres鈥?equation in Riesz spaces. J. Math. Anal. Appl. 406, 261鈥?65 (2013)View Article MATH MathSciNet 5.Batko, B., Brzd醛k, J.: A fixed point theorem and the Hyers鈥揢lam stability in Riesz spaces. Adv. Differ. Equ. 2013, 138 (2013) 6.Batko B., Tabor J.: Stability of the generalized alternative Cauchy equation. Abh. Math. Sem. Univ. Hamb. 69, 67鈥?3 (1999)View Article MATH MathSciNet 7.Dhombres J.G., Ger R.: Conditional Cauchy equations. Glasnik Mat. 13(33), 39鈥?2 (1978)MathSciNet 8.Fremlin, D.H.: Measure theory: measure algebras, vol. 3. Torres Fremlin, Colchester (2002) 9.Luxemburg W.A.J., Zaanen A.C.: Riesz spaces. North-Holland Publishing Company, Amsterdam (1971)MATH 10.Moszner Z.: On stability of some functional equations and topology of their target spaces. Annales Univ. Paed. Crac. Studia Math. XI(122), 69鈥?4 (2012)MathSciNet
作者单位:Bogdan Batko (1) (2)
1. Institute of Mathematics, Pedagogical University of Cracow, Podchora抬偶ych 2, 30-084, Krak贸w, Poland 2. Department of Mathematics, WSB-NLU, Zielona 27, 33-300, Nowy Sa抬cz, Poland
刊物类别:Mathematics and Statistics
刊物主题:Mathematics Analysis Combinatorics
出版者:Birkh盲user Basel
ISSN:1420-8903
文摘
We describe a method of extending certain stability results valid for real-valued functions to the class of functions with range in an f-algebra. The method is based on the Spectral Representation Theory for Riesz spaces. Details will be presented for the multiplicative Dhombres functional equation $$(F(x) + F(y))(F(x + y) - F(x) - F(y)) = 0.$$