Nonlinear stability of \(\rho\)-functional equations in latticetic random Banach lattice spaces
Summary: In this paper, we prove the generalized nonlinear stability of the first and second of the following \(\rho\)-functional equations, \[ G(| a| \Delta_{\mathcal A}^\ast| b|) \Delta_{\mathcal B}^\ast G(| a|\Delta_{\mathcal A}^{\ast\ast}| b|) - G(| a|) \Delta_{\mathcal B}^{\ast\ast} G(| b|) = \rho (2 \left[G\left(\frac{| a| \Delta_{\mathcal A}^\ast| b |}{2}\right) \Delta_{\mathcal B}^\ast G \left(\frac{| a| \Delta_{\mathcal A}^{\ast\ast}| b|}{2}\right)\right] - G(| a|) \Delta_{\mathcal B}^{\ast\ast} G(| b|)), \] and \[ 2 \left [G \left(\frac{| a|\Delta_{\mathcal A}^\ast| b|}{2}\right)\Delta_{\mathcal B}^\ast G \left(\frac{| a|\Delta_{\mathcal A}^{\ast\ast}| b|}{2}\right)\right]-G(| a|) \Delta_{\mathcal B}^{\ast\ast} G(| b|) = \rho \left(G(| a| \Delta_{\mathcal A}^\ast | b |)\Delta_{\mathcal B}^\ast G(| a|\Delta_{\mathcal A}^{\ast\ast}| b|)-G(| a |)\Delta_{\mathcal B}^{\ast\ast}G (| b|)\right) \] in latticetic random Banach lattice spaces, where \(\rho\) is a fixed real or complex number with \(\rho \neq 1\).
scientific article; zbMATH DE number 6916896