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STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS IN RANDOM NORMED SPACES  

Schin, Seung Won (Seoul Science High School)
Ki, DoHyeong (Seoul Science High School)
Chang, JaeWon (Seoul Science High School)
Kim, Min June (Seoul Science High School)
Park, Choonkil (Department of Mathematics Hanyang University)
Publication Information
Korean Journal of Mathematics / v.18, no.4, 2010 , pp. 395-407 More about this Journal
Abstract
In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations $$cf\(\sum_{i=1}^{n}x_i\)+\sum_{j=2}^{n}f\(\sum_{i=1}^{n}x_i-(n+c-1)x_j\)\\=(n+c-1)\(f(x_1)+c\sum_{i=2}^{n}f(x_i)+\sum_{i<j,j=3}^{n}\(\sum_{i=2}^{n-1}f(x_i-x_j\)\),\\Q\(\sum_{i=1}^{n}d_ix_i\)+\sum_{1{\leq}i<j{\leq}n}d_id_jQ(x_i-x_j)=\(\sum_{i=1}^{n}d_i\)\(\sum_{i=1}^{n}d_iQ(x_i)\)$$ in random normed spaces.
Keywords
random Banach space; quadratic functional equation; generalized Hyers-Ulam stability; quadratic mapping;
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Times Cited By KSCI : 1  (Citation Analysis)
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