A fixed point approach to orthogonal stability of an additive-cubic functional equation. (English) Zbl 1367.39005

Murali, R.; Deboral, M.; Raj, A. Antony

Int. J. Adv. Appl. Math. Mech. 3, No. 4, 1-8 (2016).

Summary: Using fixed point method, we prove the Hyers-Ulam stability of the orthogonally additive-cubic functional equation \[ f(2x+y)+f(2x-y)-f(4x)=2f(x+y)+2f(x-y)-8f(2x)+10f(x)-2f(-x) \] for all \(x\), \(y\) with \(x \bot y\).

MSC:

39B22	Functional equations for real functions
39B55	Orthogonal additivity and other conditional functional equations
39B82	Stability, separation, extension, and related topics for functional equations

Keywords:

Hyers-Ulam stability; additive and cubic functional equations; fixed point method; orthogonality space