Orthogonalities and functional equations
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| 008 | 210128e20150401xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0288-0 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0288-0 | ||
| 100 | 1 | |a Sikorska |D Justyna |u Institute of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland |4 aut | |
| 245 | 1 | 0 | |a Orthogonalities and functional equations |h [Elektronische Daten] |c [Justyna Sikorska] |
| 520 | 3 | |a In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations. | |
| 540 | |a The Author(s), 2014 | ||
| 690 | 7 | |a Orthogonality |2 nationallicence | |
| 690 | 7 | |a Birkhoff orthogonality |2 nationallicence | |
| 690 | 7 | |a James isosceles orthogonality |2 nationallicence | |
| 690 | 7 | |a approximate orthogonality |2 nationallicence | |
| 690 | 7 | |a inner product space |2 nationallicence | |
| 690 | 7 | |a normed space |2 nationallicence | |
| 690 | 7 | |a Hilbert modules |2 nationallicence | |
| 690 | 7 | |a norm derivative |2 nationallicence | |
| 690 | 7 | |a semi-inner product |2 nationallicence | |
| 690 | 7 | |a Cauchy equation |2 nationallicence | |
| 690 | 7 | |a quadratic equation |2 nationallicence | |
| 690 | 7 | |a exponential equation |2 nationallicence | |
| 690 | 7 | |a orthogonal additivity |2 nationallicence | |
| 690 | 7 | |a stability |2 nationallicence | |
| 690 | 7 | |a orthogonality equation |2 nationallicence | |
| 690 | 7 | |a orthogonality preserving property |2 nationallicence | |
| 690 | 7 | |a linear preservers |2 nationallicence | |
| 690 | 7 | |a isometry |2 nationallicence | |
| 690 | 7 | |a approximate isometry |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/2(2015-04-01), 215-277 |x 0001-9054 |q 89:2<215 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0288-0 |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/s00010-014-0288-0 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Sikorska |D Justyna |u Institute of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/2(2015-04-01), 215-277 |x 0001-9054 |q 89:2<215 |1 2015 |2 89 |o 10 | ||