Spectral representation theory and stability of the multiplicative Dhombres functional equation in f -algebras
| LEADER | caa a22 4500 | ||
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| 001 | 605508313 | ||
| 003 | CHVBK | ||
| 005 | 20210128100636.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150601xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-013-0234-6 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-013-0234-6 | ||
| 100 | 1 | |a Batko |D Bogdan |u Institute of Mathematics, Pedagogical University of Cracow, 30-084, Kraków, Podchora̧żych 2, Poland |4 aut | |
| 245 | 1 | 0 | |a Spectral representation theory and stability of the multiplicative Dhombres functional equation in f -algebras |h [Elektronische Daten] |c [Bogdan Batko] |
| 520 | 3 | |a 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. | |
| 540 | |a The Author(s), 2014 | ||
| 690 | 7 | |a Riesz space |2 nationallicence | |
| 690 | 7 | |a f -algebra |2 nationallicence | |
| 690 | 7 | |a Spectral Representation Theory |2 nationallicence | |
| 690 | 7 | |a Ogasawara-Maeda Spectral Representation Theorem |2 nationallicence | |
| 690 | 7 | |a Stability |2 nationallicence | |
| 690 | 7 | |a Conditional Cauchy Equation |2 nationallicence | |
| 690 | 7 | |a Dhombres equation |2 nationallicence | |
| 690 | 7 | |a Approximation |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 543-554 |x 0001-9054 |q 89:3<543 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-013-0234-6 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-013-0234-6 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Batko |D Bogdan |u Institute of Mathematics, Pedagogical University of Cracow, 30-084, Kraków, Podchora̧żych 2, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 543-554 |x 0001-9054 |q 89:3<543 |1 2015 |2 89 |o 10 | ||