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

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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 HyersUlamRassias stability of the Jensen \(\rho\)functional inequalities in complex Banach spaces
and prove the HyersUlamRassias 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, 3variable Jensen \(\rho\)functional inequalities and equations, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 59956003
AMA Style
Lu Gang, Liu Qi, Jin Yuanfeng, Xie Jun, 3variable Jensen \(\rho\)functional inequalities and equations. J. Nonlinear Sci. Appl. (2016); 9(12):59956003
Chicago/Turabian Style
Lu, Gang, Liu, Qi, Jin, Yuanfeng, Xie, Jun. "3variable Jensen \(\rho\)functional inequalities and equations." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 59956003
Keywords
 Jensen functional inequalities
 HyersUlamRassias stability
 complex Banach spaces.
MSC
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