Stability of a functional equation deriving from quadratic and additive functions in quasi-Banach spaces
Copyright policy )Stability of a functional equation deriving from quadratic and additive functions in quasi-Banach spaces
The authors establish the general solution of the functional equation \[ f(2x+y)+f(2x-y)=f(x+y)+f(x-y)+2f(2x)-2f(x) \] deriving from quadratic and additive functions. They also prove the Hyers-Ulam-Rassias stability for the above equation in quasi Banach spaces. The authors missed citing the paper by \textit{J. Tabor} [Ann. Pol. Math. 83, No. 3, 243--255 (2004; Zbl 1101.39021)], which contains the first result about the stability of quasi-Banach spaces.
- University of Mohaghegh Ardabili Iran (Islamic Republic of)
Applied Mathematics, Stability, separation, extension, and related topics for functional equations, Hyers–Ulam–Rassias stability, Quasi-Banach space, quasi-Banach spaces, Quadratic function, p-Banach space, Additive function, Functional equations for functions with more general domains and/or ranges, quadratic functional, Hyers-Ulam-Rassias stability, Analysis, additive functional
Applied Mathematics, Stability, separation, extension, and related topics for functional equations, Hyers–Ulam–Rassias stability, Quasi-Banach space, quasi-Banach spaces, Quadratic function, p-Banach space, Additive function, Functional equations for functions with more general domains and/or ranges, quadratic functional, Hyers-Ulam-Rassias stability, Analysis, additive functional
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