- Hacettepe Journal of Mathematics and Statistics
- Vol: 40 Issue: 5
- FUZZY STABILITY OF A FUNCTIONAL EQUATION RELATED TO INNER PRODUCT SPACES
FUZZY STABILITY OF A FUNCTIONAL EQUATION RELATED TO INNER PRODUCT SPACES
Authors : Sun Young Jang, Choonkil Park
Pages : 711-723
View : 15 | Download : 6
Publication Date : 2011-05-01
Article Type : Research
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 Xm i,j=1 kxi − xjk 2 = 2m Xm i=1 kxik 2 , Xm i=1 xi = 0, for a fixed integer m ≥ 3. By the above equality, we define the following functional equation (0.1) Xm i,j=1 f(xi − xj ) = 2m Xmi=1 f(xi), Xm i=1 xi = 0. In this paper, we prove the generalized Hyers-Ulam stability of the functional equation (0.1) in fuzzy Banach spaces.Keywords : Fuzzy Banach space, Functional equation related to inner product space, Generalized Hyers-Ulam stability, 2000 AMS Classification: 46 S 40