3-variable Jensen \(\rho\)-functional inequalities and equations


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.


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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


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