Quadratic \(\rho\)-functional inequalities in \(\beta\)-homogeneous normed spaces


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


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