Geodesic
The Stability of a Functional Analogue of the Wave Equation
Canadian mathematical bulletin, Tome 33 (1990) no. 4, pp. 376-385

Voir la notice de l'article provenant de la source Cambridge University Press

For h € R and φ : R2 → R define Lhφ: R2 → R by (Lhφ)(x, y) = φ (x + h, y) + φ (x — h,y) — φ (x,y + h) — φ (x,y — h) for all (x,y) € R2. The aim of the paper is to establish the following "stability" theorem concerning the functional equation if δ > 0, f : R2 → R and then there exists ɛ > 0 ami φ : R2 → R such that (Lhφ)(x, y ) = 0 for all x, y,h ∊ R and
DOI : 10.4153/CMB-1990-062-3
Mots-clés : 39B40D, 39B50, 39A11 
Bean, Michael. The Stability of a Functional Analogue of the Wave Equation. Canadian mathematical bulletin, Tome 33 (1990) no. 4, pp. 376-385. doi: 10.4153/CMB-1990-062-3
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[1] 1. Albert, Michael and Baker, John A. Functions with bounded nth differences, Ann. Polon. Math. XLIII, (1983), 93–103. Google Scholar

[2] 2. John Baker, A. An analogue of the wave equation and certain related functional equationsCanad. Math. Bull. Vol. 12, No 6, (1969), 837–846. Google Scholar

[3] 3. Baker, John A. Regularity properties of functional equations, Aequationes Math., 6(2/3), (1971), 243– 248. Google Scholar

[4] 4. Fenyö, I. Remark on a paper of J. A. Baker, Aequationes Math., 8(1/2), (1972), 103–108. Google Scholar

[5] 5. Haruki, H. On the functional equation f(x +t, y) +f(x — t,y) — f(x, y + t) +f(x, y — t), Aequationes Math. 5(1), (1970), 118–119. Google Scholar

[6] 6. Hyers, D. H. The stability of homomorphisms and related topics, Global analysis - analysis on manifolds, Teubner-Texte zur Math. 57, Teubner, Leipzig, (1983), 140–153. Google Scholar

[7] 7. McKiernan, M. A. The general solution of some finite difference equations analogous to the wave equation, Aequationes Math. 8(3), (1972), 263–266. Google Scholar

[8] 8. Ostrowski, A. Mathematische Miszellen, XIV: Über die Funktionalgleichung der Exponential-function und verwandte Functionalgleichungen, Jber. Deutsch. Math.-Verein 38, (1929), 54–62. Google Scholar

[9] 9. Steinhaus Sur les distances des points dans les ensembles de mesure positive, Fund. Math. 1, (1920), 93–104. Google Scholar

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