Generalized quadratic mappings in 2d variables
- Title
- Generalized quadratic mappings in 2d variables
- Author
- 박춘길
- Keywords
- Hyers-Ulam stability; quadratic mapping; functional equation
- Issue Date
- 2011-03
- Publisher
- The Kangwon-Kyungki Mathematical Society
- Citation
- Korean Journal of Mathematics, 2011, 19(1), P.17-24(8)
- Abstract
- Let X, Y be vector spaces. It is shown that if an even mapping $f:X{\rightarrow}Y$ satisfies f(0) = 0, and $$2(_{2d-2}C_{d-1}-_{2d-2}C_d)f\({\sum_{j=1}^{2d}}x_j\)+{\sum_{{\iota}(j)=0,1,{{\small\sum}_{j=1}^{2d}}{\iota}(j)=d}}\;f\({\sum_{j=1}^{2d}}(-1)^{{\iota}(j)}x_j\)=2(_{2d-1}C_d+_{2d-2}C_{d-1}-_{2d-2}C_d){\sum_{j=1}^{2d}}f(x_j)$$ for all $x_1$, ${\cdots}$, $x_{2d}{\in}X$, then the even mapping $f:X{\rightarrow}Y$ is quadratic. Furthermore, we prove the Hyers-Ulam stability of the above functional equation in Banach spaces.
- URI
- http://koreascience.or.kr/article/ArticleFullRecord.jsp?cn=E1KKMK_2011_v19n1_17
- ISSN
- 1975-5015
- DOI
- 10.11568/kjm.2011.19.1.017
- Appears in Collections:
- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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