Quadratic \(\rho\)-functional inequalities in \(\beta\)-homogeneous normed spaces
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Authors
Yuanfeng Park
- Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea.
Yinhua Lu
- Department of Mathematics, School of Science, ShenYang University of Technology, Shenyang 110870, P. R. China.
- Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China.
Gang Cui
- Department of Mathematics, Yanbian University, Yanji 133001, P. R. China.
Choonkil Jin
- Department of Mathematics, Yanbian University, Yanji 133001, P. R. China.
Abstract
In this paper, we solve the quadratic \(\rho\)-functional inequalities
\[\|f(x+y)+f(x-y)-2f(x)-2f(y)\|\leq\|\rho(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y))\|,\]
where \(\rho\) is a fixed complex number with \(|\rho|<1\), and\[\|4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)\|\leq\|\rho(f(x+y)+f(x-y)-2f(x)-2f(y))\|,\]
where \(\rho\) is a fixed complex number with \(|\rho|<1\).
Using the direct method, we prove the Hyers-Ulam stability of the quadratic \(\rho\)-functional inequalities (1) and (2) in \(\beta\)-
homogeneous complex Banach spaces.
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ISRP Style
Yuanfeng Park, Yinhua Lu, Gang Cui, Choonkil Jin, Quadratic \(\rho\)-functional inequalities in \(\beta\)-homogeneous normed spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 1, 104--110
AMA Style
Park Yuanfeng, Lu Yinhua, Cui Gang, Jin Choonkil, Quadratic \(\rho\)-functional inequalities in \(\beta\)-homogeneous normed spaces. J. Nonlinear Sci. Appl. (2017); 10(1):104--110
Chicago/Turabian Style
Park, Yuanfeng, Lu, Yinhua, Cui, Gang, Jin, Choonkil. "Quadratic \(\rho\)-functional inequalities in \(\beta\)-homogeneous normed spaces." Journal of Nonlinear Sciences and Applications, 10, no. 1 (2017): 104--110
Keywords
- Hyers-Ulam stability
- \(\beta\)-homogeneous space
- quadratic \(\rho\)-functional inequality.
MSC
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