caa a22 4500 605508739 CHVBK 20210128100638.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00010-014-0295-1 doi (NATIONALLICENCE)springer-10.1007/s00010-014-0295-1 The inhomogeneous general linear functional equation [Elektronische Daten] [Wolfgang Prager, Jens Schwaiger] Given real nonzero coefficients a, A, b, B, a real parameter c and an inhomogeneity $${\varphi : \mathbb{R}\times\mathbb{R} \rightarrow \mathbb{R}}$$ φ : R × R → R , we present necessary and sufficient conditions for the existence and uniqueness of solutions of the equation $${f(ax+by+c) - Af(x) - Bf(y) = \varphi(x,y)}$$ f ( a x + b y + c ) - A f ( x ) - B f ( y ) = φ ( x , y ) . The solutions of this equation are given explicitly for each of the various cases emerging from the possibilities concerning the arithmetic nature of the four coefficients and the algebraic relationships between them. Springer Basel, 2014 Inhomogeneous linear functional equation nationallicence system offunctional equations nationallicence Prager Wolfgang Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens Universität, Heinrichstraße 36, 8010, Graz, Austria aut Schwaiger Jens Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens Universität, Heinrichstraße 36, 8010, Graz, Austria aut Aequationes mathematicae Springer Basel 89/4(2015-08-01), 1167-1187 0001-9054 89:4<1167 2015 89 10 https://doi.org/10.1007/s00010-014-0295-1 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/s00010-014-0295-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Prager Wolfgang Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens Universität, Heinrichstraße 36, 8010, Graz, Austria aut NATIONALLICENCE 700 1- Schwaiger Jens Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens Universität, Heinrichstraße 36, 8010, Graz, Austria aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/4(2015-08-01), 1167-1187 0001-9054 89:4<1167 2015 89 10