Orthogonal stability of functional equations with the fixed point alternativeopen access
- Authors
- Park, Choonkil; Cho, Yeol Je; Lee, Jung Rye
- Issue Date
- Oct-2012
- Publisher
- SPRINGEROPEN
- Keywords
- Hyers-Ulam stability; orthogonally (Jensen additive, Jensen quadratic, cubic, quartic) functional equation; fixed point; orthogonality module over Banach algebra; orthogonality space
- Citation
- ADVANCES IN DIFFERENCE EQUATIONS, pp.1 - 17
- Indexed
- SCIE
SCOPUS
- Journal Title
- ADVANCES IN DIFFERENCE EQUATIONS
- Start Page
- 1
- End Page
- 17
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/164526
- DOI
- 10.1186/1687-1847-2012-173
- ISSN
- 1687-1839
- Abstract
- In this paper, we investigate the orthogonal stability of functional equations in orthogonality modules over a unital Banach algebra. Using a fixed point method, we prove the Hyers-Ulam stability of the orthogonally Jensen additive functional equation 2f (x + y /2) = f (x) + f (y), the orthogonally Jensen quadratic functional equation 2f (x + y /2) + 2f (x - y /2) = f (x) + f (y), the orthogonally cubic functional equation f (2x + y) + f (2x - y) = 2f (x + y) + 2f (x - y) + 12f (x), and the orthogonally quartic functional equation f (2x + y) + f (2x - y) = 4f (x + y) + 4f (x - y) + 24f (x) - 6f (y) for all x, y with x perpendicular to y, where perpendicular to is the orthogonality in the sense of Ratz.
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