Let $\mathcal{G}$ be an abelian group with a metric $d, \mathcal{E}$ be a normed space and $f :\mathcal{G} \longrightarrow \mathcal{E}$ be a given function. We define difference $C_{3,1} f $ by the formula $$C_{3,1} f(x,y) = 3f(x + y) + 3f(x − y) + 48f(x) − f(3x + y) − f(3x − y)$$ for every $x,y \in \mathcal{G}$. Under some assumptions about $f$ and $C_{3,1} f $, we show that if $C_{3,1} f $ is Lipschitz, then there exists a cubic function $C :\mathcal{G} \longrightarrow \mathcal{E}$ such that $f − C$ is Lipschitz with the same constant. Moreover, we study the approximation of the equality $C_{3,1} f(x,y) = 0$ in the Lipschitz norms.
Dashti,M and Khodaei,H . (2020). A new type of approximation for cubic functional equations in Lipschitz spaces. International Journal of Nonlinear Analysis and Applications, 11(1), 291-300. doi: 10.22075/ijnaa.2020.4277
MLA
Dashti,M , and Khodaei,H . "A new type of approximation for cubic functional equations in Lipschitz spaces", International Journal of Nonlinear Analysis and Applications, 11, 1, 2020, 291-300. doi: 10.22075/ijnaa.2020.4277
HARVARD
Dashti M, Khodaei H. (2020). 'A new type of approximation for cubic functional equations in Lipschitz spaces', International Journal of Nonlinear Analysis and Applications, 11(1), pp. 291-300. doi: 10.22075/ijnaa.2020.4277
CHICAGO
M Dashti and H Khodaei, "A new type of approximation for cubic functional equations in Lipschitz spaces," International Journal of Nonlinear Analysis and Applications, 11 1 (2020): 291-300, doi: 10.22075/ijnaa.2020.4277
VANCOUVER
Dashti M, Khodaei H. A new type of approximation for cubic functional equations in Lipschitz spaces. IJNAA. 2020;11(1):291-300. doi: 10.22075/ijnaa.2020.4277
International Journal of Nonlinear Analysis and Applications