# 3-variable Jensen $\rho$-functional inequalities and equations

Volume 9, Issue 12, pp 5995--6003
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### Authors

Gang Lu - Department of Mathematics, School of Science, Shenyang University of Technology, Shenyang 110870, P. R. China. Qi Liu - Department of Mathematics, School of Science, Shenyang University of Technology, Shenyang 110870, P. R. China. Yuanfeng Jin - Department of Mathematics, Yanbian University, Yanji 133001, P. R. China. Jun Xie - Department of Mathematics, School of Science, Shenyang University of Technology, Shenyang 110870, P. R. China.

### Abstract

In this paper, we introduce and investigate Jensen $\rho$-functional inequalities associated with the following Jensen functional equations $f(x + y + z) + f(x + y - z) - 2f(x) - 2f(y) = 0,\\ f(x + y + z) - f(x - y - z) - 2f(y) - 2f(z) = 0.$ We prove the Hyers-Ulam-Rassias stability of the Jensen $\rho$-functional inequalities in complex Banach spaces and prove the Hyers-Ulam-Rassias stability of the Jensen $\rho$-functional equations associated with the $\rho$- functional inequalities in complex Banach spaces.

### Share and Cite

##### ISRP Style

Gang Lu, Qi Liu, Yuanfeng Jin, Jun Xie, 3-variable Jensen $\rho$-functional inequalities and equations, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 5995--6003

##### AMA Style

Lu Gang, Liu Qi, Jin Yuanfeng, Xie Jun, 3-variable Jensen $\rho$-functional inequalities and equations. J. Nonlinear Sci. Appl. (2016); 9(12):5995--6003

##### Chicago/Turabian Style

Lu, Gang, Liu, Qi, Jin, Yuanfeng, Xie, Jun. "3-variable Jensen $\rho$-functional inequalities and equations." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 5995--6003

### Keywords

• Jensen functional inequalities
• Hyers-Ulam-Rassias stability
• complex Banach spaces.

•  39B62
•  39B52
•  39B82

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