On an equation characterizing multi-additive-quadratic mappings and its Hyers–Ulam stability

On Stability and Hyperstability of an Equation Characterizing Multi-Cauchy–Jensen Mappings

“…This result is a tool for obtaining a generalized Hyers-Ulam stability or hyperstability of this equation for particular control functions, which is presented in several examples. Our results are significant counterparts of some classical outcomes from [1,11,22,23,35] and recent results from [2][3][4]10,[17][18][19][20][24][25][26][27]31,32,34,36].…”

On Hyers–Ulam stability of two functional equations in non-Archimedean spaces

“…In this section, we use Theorem 2.2 to prove the generalized Hyers-Ulam stability of an equation characterizing multi-additive-quadratic mappings in complete non-Archimedean normed spaces (its stability in Banach spaces was shown in [1]). Before we recall this characterization (obtained in [1]) and state the stability result, let us introduce an additional notation. Namely, given an m ∈ N, for any p…”

Characterization, stability and hyperstability of multi-quadratic–cubic mappings

“…In other words, we reduce the system of n equations defining the multi-quadratic-cubic mappings to obtain a single functional equation. We also prove the generalized Hyers-Ulam stability and hyperstability for multiquadratic-cubic functional equations by using the fixed point method which was used for the first time by Brzdȩk in [12]; for more applications of this approach for the stability of multi-Cauchy-Jensen, multi-additive-quadratic, multi-cubic and multi-quartic mappings in Banach spaces see [2,3,10] and [8] respectively.…”