Hyers–Ulam stability of a generalized Apollonius type quadratic mapping☆

By Chun-Gil Park, Themistocles M. Rassias. 2006

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Abstract Let X , Y be linear spaces. It is shown that if a mapping Q : X → Y satisfies the following functional equation: (0.1) Q ( ( ∑ i = 1 n z i ) − ( ∑ i = 1 n x i ) ) + Q ( ( ∑ i = 1 n z i ) − ( ∑ i = 1 n y i ) ) = 1 2 Q ( ( ∑ i = 1 n x i ) − ( ∑ i = 1 n y i ) ) + 2 Q ( ( ∑ i = 1 n z i ) − ( ∑ i = 1 n x i ) + ( ∑ i = 1 n y i ) 2 ) then the mapping Q : X → Y is quadratic. We moreover prove the Hyers–Ulam stability of the functional equation (0.1) in Banach spaces.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/f9dacdf4626b690fc13a2ee141b62f41b4e9dd5a