an:07086055
Zbl 1417.39085
Phochai, Theerayoot; Saejung, Satit
The hyperstability of general linear equation via that of Cauchy equation
EN
Aequationes Math. 93, No. 4, 781-789 (2019).
0001-9054 1420-8903
2019
j
39B82 39B62 47H14 47J20
hyperstability; general linear equation; Cauchy equation
The task of a hyperstability problem is to understand when a function which approximately satisfies a functional equation is also a solution of it. \textit{M. Piszczek} [Aequationes Math. 88, No. 1--2, 163--168 (2014; Zbl 1304.39033)] proved a hyperstability result for general linear equation \(f(ax + by) = Af(x) + Bf(y)\). \textit{J. Brzdęk} [Acta Math. Hung. 141, No. 1--2, 58--67 (2013; Zbl 1313.39037)] and proved the hyperstability of the Cauchy equation \(f(x+y)=f(x)+f(y)\). In the paper under review, the authors show that the result of Piszczek can be deduced from that of Brzdęk.
Mohammad Sal Moslehian (Mashhad)
1304.39033; 1313.39037