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Hom-derivations in \(C*\)-ternary algebras. (English) Zbl 07343745
Summary: In this paper, we introduce and solve the following additive \((\rho_1,\rho_2)\)-functional inequalities \[ \begin{split}\Vert f(x+y+z)-f(x)-f(y)-f(z)\Vert\\ \leq\Vert \rho_1(f(x+z)-f(x)-f(z)\Vert +\Vert\rho_2(f(y+z)-f(y)-f(z))\Vert, \end{split} \] where \(\rho_1\) and \(\rho_2\) are fixed nonzero complex numbers with \(|\rho_1|+|\rho_2| < 2\). Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the above additive \((\rho_1,\rho_2)\)-functional inequality in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of hom-derivations in \(C*\)-ternary algebras.
MSC:
39B62 Functional inequalities, including subadditivity, convexity, etc.
16W25 Derivations, actions of Lie algebras
39B82 Stability, separation, extension, and related topics for functional equations
47H10 Fixed-point theorems
39B52 Functional equations for functions with more general domains and/or ranges
47B47 Commutators, derivations, elementary operators, etc.
46L57 Derivations, dissipations and positive semigroups in \(C^*\)-algebras
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