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- Title
Stability of Cubic Functional Equation in the Spaces of Generalized Functions.
- Authors
Young-Su Lee; Soon-Yeong Chung
- Abstract
The article focuses on the stability of cubic functional equation in the spaces of generalized functions. It is proved that the Hyers-Ulam-Rassias stability theorem cubic functional equation of the cubic functional equation f ( ax + y ) + f ( ax - y ) = af ( x + y ) + af ( x - y ) + 2a(a2 - 1 ) f ( x ) for fixed integer a with a ≠ 0, ± 1 in the spaces of Schwartz tempered distributions and Fourier hyperfunctions. It is mentioned that in 1940, questions concerning the stability of group homomorphisms was solved by Hyers, assuming that G1 and G2 are Banach spaces. It is said that in 1978, Rassias generalized Hyers' result to the unbounded Cauchy difference.
- Subjects
FUNCTIONAL equations; THEORY of distributions (Functional analysis); SCHWARTZ distributions; HYPERFUNCTIONS; HOMOMORPHISMS; BANACH spaces; PARTIAL differential equations; MATHEMATICAL research; MATHEMATICAL analysis
- Publication
Journal of Inequalities & Applications, 2007, Vol 2007, Issue 1, p1
- ISSN
1025-5834
- Publication type
Article
- DOI
10.1155/2007/79893