Superstability of some Pexider-type functional equation
The author studies the superstability of the sine functional equation on the basis of the following Pexider-type functional equation \[ f(x+ y)+ g(x- y)= \lambda\cdot h(x)k(y), \] where \(k\) is a constant, which is actually a mixed functional equation. The problem studied in this paper has its origin in Ulam's problem for approximate homomorphism with its subsequent stability theorems of D. H. Hyers, T. Aoki, D. G. Bourgin, Th. M. Rassias and P. Găvruta. Reviewer's note: The following two books are useful treatises in the subject of the paper with several results and a number of applications of interdisciplinary character: {\parindent6.5mm \begin{itemize}\item[(1)] \textit{D. H. Hyers}, \textit{G. Isac} and \textit{Th. M. Rassias} [Stability of functional equations in several variables. Progress in Nonlinear Differential Equations and their Applications. 34. Boston, MA: Birkhäuser (1998; Zbl 0907.39025)]. \item[(2)] \textit{Pl. Kannappan} [Functional equations and inequalities with applications. Springer Monographs in Mathematics. New York, NY: Springer (2009; Zbl 1178.39032)]. \end{itemize}}
scientific article; zbMATH DE number 5823211
scientific article