The inhomogeneous general linear functional equation
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| 024 | 7 | 0 | |a 10.1007/s00010-014-0295-1 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0295-1 | ||
| 245 | 0 | 4 | |a The inhomogeneous general linear functional equation |h [Elektronische Daten] |c [Wolfgang Prager, Jens Schwaiger] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Basel, 2014 | ||
| 690 | 7 | |a Inhomogeneous linear functional equation |2 nationallicence | |
| 690 | 7 | |a system offunctional equations |2 nationallicence | |
| 700 | 1 | |a Prager |D Wolfgang |u Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens Universität, Heinrichstraße 36, 8010, Graz, Austria |4 aut | |
| 700 | 1 | |a Schwaiger |D Jens |u Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens Universität, Heinrichstraße 36, 8010, Graz, Austria |4 aut | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/4(2015-08-01), 1167-1187 |x 0001-9054 |q 89:4<1167 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0295-1 |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/s00010-014-0295-1 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Prager |D Wolfgang |u Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens Universität, Heinrichstraße 36, 8010, Graz, Austria |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Schwaiger |D Jens |u Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens Universität, Heinrichstraße 36, 8010, Graz, Austria |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/4(2015-08-01), 1167-1187 |x 0001-9054 |q 89:4<1167 |1 2015 |2 89 |o 10 | ||