Duplicating the cube and functional equations

On stability of the functional equation of p-Wright affine functions in (2, α)-Banach spaces

“…which has been investigated by Najati and Park in [32]. The cases of more arbitrary p were studied in [15] (see also [25]). We prove some results concerning the Hyers-Ulam stability of (1).…”

Stability of the equation of the p-Wright affine functions

“…It remains to show the statement concerning the uniqueness of G. So suppose that M 0 ∈ (0, ∞) and G 1 : X → Y is a solution to (1.1) with 12) and, by (2.2), 13) where…”

“…(1.1) takes the form f (2x + y) + f (x + 2y) = f (3x) + f (3y), (1.2) which has been investigated by Najati and Park [18]; in particular, they proved some results on its stability and applied them in the investigation of the generalized (σ, τ )-Jordan derivations on Banach algebras. The cases of more arbitrary p were studied in [4,5,15] (see also [9,13]). We prove some results concerning the Hyers-Ulam stability and superstability of (1.1).…”

Recent results on functional equations in a single variable, perspectives and open problems

“…For some problems reducing to (4.2) or related to it see [10] by J. A. Baker, [77] by G. Derfel, [129], and [274] by Wei-Bin Zeng. Non-negative and measurable solutions of the even more general equation…”