Geodesic
Quadratic $\rho$-functional inequalities in $\beta$-homogeneous normed spaces
Park, Yuanfeng1 ; Lu, Yinhua2 ; Cui, Gang3 ; Jin, Choonkil3
1 Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea
2 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
3 Department of Mathematics, Yanbian University, Yanji 133001, P. R. China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 104-110.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.01.10
Classification : 39B62, 39B72, 39B52, 39B82
Keywords: Hyers-Ulam stability, \(\beta\)-homogeneous space, quadratic \(\rho\)-functional inequality.

Park, Yuanfeng 1 ; Lu, Yinhua 2 ; Cui, Gang 3 ; Jin, Choonkil 3

1 Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea
2 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
3 Department of Mathematics, Yanbian University, Yanji 133001, P. R. China 
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Park, Yuanfeng; Lu, Yinhua; Cui, Gang; Jin, Choonkil. Quadratic \(\rho\)-functional inequalities in \(\beta\)-homogeneous normed spaces. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 1, p. 104-110. doi : 10.22436/jnsa.010.01.10. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.01.10/

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