caa a22 4500 605508313 CHVBK 20210128100636.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00010-013-0234-6 doi (NATIONALLICENCE)springer-10.1007/s00010-013-0234-6 Batko Bogdan Institute of Mathematics, Pedagogical University of Cracow, 30-084, Kraków, Podchora̧żych 2, Poland aut Spectral representation theory and stability of the multiplicative Dhombres functional equation in f -algebras [Elektronische Daten] [Bogdan Batko] 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 $$(F(x) + F(y))(F(x + y) - F(x) - F(y)) = 0.$$ ( F ( x ) + F ( y ) ) ( F ( x + y ) - F ( x ) - F ( y ) ) = 0 . In this note we use the Ogasawara-Maeda Spectral Representation Theorem for Riesz spaces which will be firstly adapted to the f-algebras reality. The Author(s), 2014 Riesz space nationallicence f -algebra nationallicence Spectral Representation Theory nationallicence Ogasawara-Maeda Spectral Representation Theorem nationallicence Stability nationallicence Conditional Cauchy Equation nationallicence Dhombres equation nationallicence Approximation nationallicence Aequationes mathematicae Springer Basel 89/3(2015-06-01), 543-554 0001-9054 89:3<543 2015 89 10 https://doi.org/10.1007/s00010-013-0234-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-013-0234-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Batko Bogdan Institute of Mathematics, Pedagogical University of Cracow, 30-084, Kraków, Podchora̧żych 2, Poland aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/3(2015-06-01), 543-554 0001-9054 89:3<543 2015 89 10