Random stability of a functional equation associated with inner product: a fixed point approach
- Title
- Random stability of a functional equation associated with inner product: a fixed point approach
- Author
- 박춘길
- Keywords
- Additive mapping; Fixed point; Functional equation related to inner product space; Hyers-Ulam stability; Quadratic mapping; Random Banach space
- Issue Date
- 2012-01
- Publisher
- WATAM PRESS
- Citation
- DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS, Vol.19 No.1 [2012], pp.65-80
- Abstract
- Th.M. Rassias [Bull. Sci. Math. 108 (1984), 95{99] proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed positive integer l2l12l∑ 2li= 1xi2+∑2li=1xi ? 12l∑2lj=1xj2=∑ 2li=1?xi? 2holds for all x1; ; x2l ? V. For the above equality, we can define the following functionalequation 2lf(12l∑2li=1xi)+∑2li=1fxi ? 12l∑2lj=1xj =∑2li=1f(xi); (1) whose solution is realized as the sum of an additive mapping and a quadratic mapping. Using fixed point method, we prove the Hyers-Ulam stability of the functional equation (1) in random Banach spaces.
- URI
- https://www.kci.go.kr/kciportal/co/download/popup/poDownload.kci?storFileBean.orteFileId=KCI_FI001282983https://repository.hanyang.ac.kr/handle/20.500.11754/70563
- ISSN
- 1201-3390
- Appears in Collections:
- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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