2018
Том 70
№ 8

# Rassias J. M.

Articles: 3
Brief Communications (English)

### Approximation of general α-cubic functional equations in 2-Banach spaces

Ukr. Mat. Zh. - 2016. - 68, № 10. - pp. 1430-1436

We introduce a new \alpha -cubic functional equation and investigate the generalized Hyers – Ulam stability of this functional equation in 2-Banach spaces.

Article (English)

### θ-Centralizers on Semiprime Banach *-algebras

Ukr. Mat. Zh. - 2014. - 66, № 2. - pp. 269–278

We generalize the celebrated theorem of Johnson and prove that every left θ -centralizer on a semisimple Banach algebra with left approximate identity is continuous. We also investigate the generalized Hyers–Ulam–Rassias stability and the superstability of θ -centralizers on semiprime Banach *-algebras.

Article (English)

### A generalized mixed type of quartic, cubic, quadratic and additive functional equation

Ukr. Mat. Zh. - 2011. - 63, № 3. - pp. 399-415

We determine the general solution of the functional equation $f(x + ky) + f(x — ky) = g(x + y) + g(x — y) + h(x) + \tilde{h}(y)$ forfixed integers $k$ with $k \neq 0, \pm 1$ without assuming any regularity condition on the unknown functions $f, g, h, \tilde{h}$. The method used for solving these functional equations is elementary but exploits an important result due to Hosszii. The solution of this functional equation can also be determined in certain type of groups using two important results due to Szekelyhidi.