Spectral representation theory and stability of the multiplicative Dhombres functional equation in f-algebras

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• 作者：Bogdan Batko
• 关键词：Primary 39B82 ; Secondary 46A40 ; Riesz space ; f ; algebra ; Spectral Representation Theory ; Ogasawara鈥揗aeda Spectral Representation Theorem ; Stability ; Conditional Cauchy Equation ; Dhombres equation ; Approximation
• 刊名：Aequationes Mathematicae
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：89
• 期：3
• 页码：543-554
• 全文大小：467 KB
• 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 $$(F(x) + F(y))(F(x + y) - F(x) - F(y)) = 0.$$