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

Lu, Gang¹ ; Liu, Qi¹ ; Jin, Yuanfeng² ; Xie, Jun¹

¹ Department of Mathematics, School of Science, Shenyang University of Technology, Shenyang 110870, P. R. China
² Department of Mathematics, Yanbian University, Yanji 133001, P. R. China

Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 12, p. 5995-6003.

Résumé

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.

Détail

DOI : 10.22436/jnsa.009.12.07

Classification : 39B62, 39B52, 39B82
Keywords: Jensen functional inequalities, Hyers-Ulam-Rassias stability, complex Banach spaces.

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