Quadratic \(\rho\)-functional inequalities in complex matrix normed spaces
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Authors
Zhihua Wang
- School of Science, Hubei University of Technology, Wuhan, Hubei 430068, P. R. China.
Choonkil Park
- Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Republic of Korea.
Abstract
In this paper, we solve the following quadratic \(\rho\) -functional inequalities
\[\|f(x + y)+f(x - y) - 2f(x) - 2f(y)\| \leq\|\rho(2f(\frac{x + y}{2}) + 2f(\frac{x - y}{2}) - f(x) - f(y))\|,\]
where \(\rho\) is a fixed complex number with \(|\rho|< 1\), and
\[\|2f(\frac{x + y}{2}) + 2f(\frac{x - y}{2}) - f(x) - f(y)\| \leq\|\rho(f(x + y)+f(x - y) - 2f(x) - 2f(y)\|,\]
where \(\rho\) is a fixed complex number with \(|\rho| <\frac{ 1}{2}\) . By using the direct method, we prove the Hyers-Ulam
stability of these inequalities in complex matrix normed spaces, and prove the Hyers-Ulam stability of
quadratic \(\rho\)-functional equations associated with these inequalities in complex matrix normed spaces.
Share and Cite
ISRP Style
Zhihua Wang, Choonkil Park, Quadratic \(\rho\)-functional inequalities in complex matrix normed spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 9, 5344--5352
AMA Style
Wang Zhihua, Park Choonkil, Quadratic \(\rho\)-functional inequalities in complex matrix normed spaces. J. Nonlinear Sci. Appl. (2016); 9(9):5344--5352
Chicago/Turabian Style
Wang, Zhihua, Park, Choonkil. "Quadratic \(\rho\)-functional inequalities in complex matrix normed spaces." Journal of Nonlinear Sciences and Applications, 9, no. 9 (2016): 5344--5352
Keywords
- Hyers-Ulam stability
- matrix normed space
- quadratic \(\rho\)-functional equation
- quadratic \(\rho\)-functional inequality.
MSC
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