[FORTHCOMING] Measure zero stability problem for multi-dimensional cubic functional equations

This work aims to present a novel fashion of the multi-dimensional cubic functional equations and to investigate its Hyers-Ulam stability in the setting of Banach spaces on the restricted domains under a condition as (C). Moreover, a subset $$$\Omega\subset\mathbb R^d$$$ of Lebesgue measure zero satisfying the mentioned condition is constructed. Lastly, applying this construction and by means of the Baire category theorem, an asymptotic behavior for an approximate solution of the d-dimension cubic functional equations on real numbers, is presented.

This work aims to present a novel fashion of the multi-dimensional cubic functional equations and to investigate its Hyers-Ulam stability in the setting of Banach spaces on the restricted domains under a condition as (C). Moreover, a subset $$$\Omega\subset\mathbb R^d$$$ of Lebesgue measure zero satisfying the mentioned condition is constructed. Lastly, applying this construction and by means of the Baire category theorem, an asymptotic behavior for an approximate solution of the d-dimension cubic functional equations on real numbers, is presented.

space Hyers-Ulam stability Lebesgue measure zero multi-dimensional cubic mapping

space Hyers-Ulam stability Lebesgue measure zero multi-dimensional cubic mapping