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FUZZY STABILITY OF A FUNCTIONAL EQUATION RELATED TO INNER PRODUCT SPACES
- Authors
- Jang, Sun Young; Park, Choonkil
- Issue Date
- Oct-2011
- Publisher
- University of Hacettepe
- Keywords
- Fuzzy Banach space; Functional equation related to inner product space; Generalized Hyers-Ulam stability
- Citation
- Hacettepe Journal of Mathematics and Statistics, v.40, no.5, pp 711 - 723
- Pages
- 13
- Indexed
- SCIE
SCOPUS
- Journal Title
- Hacettepe Journal of Mathematics and Statistics
- Volume
- 40
- Number
- 5
- Start Page
- 711
- End Page
- 723
- ISSN
- 1303-5010
2651-477X
- Abstract
- The fuzzy stability problems for the Cauchy quadratic functional equation and the Jensen quadratic functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Th. M. Rassias introduced the following equality Sigma(m)(i,j=1) parallel to xi - xj parallel to(2) = 2m Sigma(m)(i=1) parallel to x(i)parallel to(2), Sigma(m)(i=1) x(i) = 0, for a fixed integer m >= 3. By the above equality, we define the following functional equation (0.1) Sigma(m)(i,j=1) f(x(i) - x(j)) = 2m Sigma(m)(i=1) f(x(i)), Sigma(m)(i=1) x(i) = 0 In this paper, we prove the generalized Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.
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