On the Ulam stability of the Cauchy-Jensen equation and the additive-quadratic equation
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Authors
Jae-Hyeong Bae
- Humanitas College, Kyung Hee University, Yongin 446-701, Republic of Korea.
Won-Gil Park
- Department of Mathematics Education, College of Education, Mokwon University, Daejeon 302-729, Republic of Korea.
Abstract
In this paper, we investigate the Ulam stability of the functional equations
\[2f ( x + y; \frac{z + w}{ 2} ) = f(x; z) + f(x;w) + f(y; z) + f(y;w)\]
and
\[f(x + y; z + w) + f(x + y; z - w) = 2f(x; z) + 2f(x;w) + 2f(y; z) + 2f(y;w)\]
in paranormed spaces.
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ISRP Style
Jae-Hyeong Bae, Won-Gil Park, On the Ulam stability of the Cauchy-Jensen equation and the additive-quadratic equation, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 5, 710--718
AMA Style
Bae Jae-Hyeong, Park Won-Gil, On the Ulam stability of the Cauchy-Jensen equation and the additive-quadratic equation. J. Nonlinear Sci. Appl. (2015); 8(5):710--718
Chicago/Turabian Style
Bae, Jae-Hyeong, Park, Won-Gil. "On the Ulam stability of the Cauchy-Jensen equation and the additive-quadratic equation." Journal of Nonlinear Sciences and Applications, 8, no. 5 (2015): 710--718
Keywords
- Cauchy-Jensen mapping
- additive-quadratic mapping
- paranormed space.
MSC
References
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