Fixed point and Hyers-Ulam stability of functional equations. (English) Zbl 1252.39036

Azadi Kenary, Hassan; Shin, Dong Yun; Lee, Jung Rye; Hoseini, Habib

Int. J. Math. Anal., Ruse 5, No. 37-40, 1827-1833 (2011).

Using the fixed point method, the authors prove the generalized Hyers-Ulam stability of the following functional equation \[ f(3x\pm y)= f (x\pm y)+ 16f(x) \] in non-Archimedean normed spaces

•  Encyclopedia of Mathematics
•  Wikipedia
•  Wolfram MathWorld

. It is an interesting contribution in a basic functional equation.

Reviewer: Themistocles M. Rassias (Athens)

MSC:

39B82	Stability, separation, extension, and related topics for functional equations
46S10	Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
39B52	Functional equations for functions with more general domains and/or ranges

Keywords:

functional equations; non-Archimedean normed spaces; fixed point method; generalized Hyers-Ulam stability