caa a22 4500 605509042 CHVBK 20210128100639.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00010-014-0288-0 doi (NATIONALLICENCE)springer-10.1007/s00010-014-0288-0 Sikorska Justyna Institute of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland aut Orthogonalities and functional equations [Elektronische Daten] [Justyna Sikorska] 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. The Author(s), 2014 Orthogonality nationallicence Birkhoff orthogonality nationallicence James isosceles orthogonality nationallicence approximate orthogonality nationallicence inner product space nationallicence normed space nationallicence Hilbert modules nationallicence norm derivative nationallicence semi-inner product nationallicence Cauchy equation nationallicence quadratic equation nationallicence exponential equation nationallicence orthogonal additivity nationallicence stability nationallicence orthogonality equation nationallicence orthogonality preserving property nationallicence linear preservers nationallicence isometry nationallicence approximate isometry nationallicence Aequationes mathematicae Springer Basel 89/2(2015-04-01), 215-277 0001-9054 89:2<215 2015 89 10 https://doi.org/10.1007/s00010-014-0288-0 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/s00010-014-0288-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sikorska Justyna Institute of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/2(2015-04-01), 215-277 0001-9054 89:2<215 2015 89 10