RANDOM STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS A FIXED POINT APPROACH
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Authors
SEUNG WON SCHIN
- Seoul Science High School, Seoul 110-530, Republic of Korea.
DOHYEONG KI
- Seoul Science High School, Seoul 110-530, Republic of Korea.
JAEWON CHANG
- Seoul Science High School, Seoul 110-530, Republic of Korea.
MIN JUNE KIM
- Seoul Science High School, Seoul 110-530, Republic of Korea.
Abstract
Using the fixed point method, we prove the generalized Hyers-
Ulam stability of the following quadratic functional equations
\[cf (\sum^n_{ i=1} x_i) + \sum^n_{ j=2} f (\sum^n_{ i=1} x_i - (n + c - 1)x_j)\\
= (n + c - 1)(f(x_1) + c \sum^n _{i=2} f(x_i) + \sum^n_{ i<j,j=3} (\sum^{n-1}_{ i=2} f(x_i - x_j) )),\\
Q(\sum^n _{i=1} d_ix_i ) + \sum_{1\leq i<j\leq n} d_id_jQ(x_i - x_j) =(\sum^n_{ i=1} d_i)(\sum^n_{ i=1} d_iQ(x_i))\]
in random Banach spaces.
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ISRP Style
SEUNG WON SCHIN, DOHYEONG KI, JAEWON CHANG, MIN JUNE KIM, RANDOM STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS A FIXED POINT APPROACH, Journal of Nonlinear Sciences and Applications, 4 (2011), no. 1, 37-49
AMA Style
SCHIN SEUNG WON, KI DOHYEONG, CHANG JAEWON, KIM MIN JUNE, RANDOM STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS A FIXED POINT APPROACH. J. Nonlinear Sci. Appl. (2011); 4(1):37-49
Chicago/Turabian Style
SCHIN, SEUNG WON, KI, DOHYEONG, CHANG , JAEWON, KIM, MIN JUNE. " RANDOM STABILITY OF QUADRATIC FUNCTIONAL EQUATIONS A FIXED POINT APPROACH." Journal of Nonlinear Sciences and Applications, 4, no. 1 (2011): 37-49
Keywords
- random Banach space
- fixed point
- quadratic functional equation
- generalized Hyers-Ulam stability.
MSC
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