On the Hyers–Ulam stability of functional equations connected with additive and quadratic mappings

Abstract

We investigate some inequalities connected with the Hyers-Ulam stability of three functional equations, which have a solution of the form ϕ = a + q, where a is an additive mapping and q is a quadratic one.

Stability of a generalization of the Fréchet functional equation

“…The results we prove correspond also to some outcomes in [8,11,16,19,25]. The results in [2] as well as our main theorem have been motivated by the notion of hyperstability of functional equations (see, e.g., [3,4,5,13,20]), introduced in connection with the issue of stability of functional equations (for more details see, e.g., [14,17]).…”

On the generalized Fréchet functional equation with constant coefficients and its stability

“…Such a method has been used in, e.g., [4][5][6]10,26,30,33,34]. Moreover, the results that we provide correspond to the outcomes in [3,9,13,16,18,21,24,25,31,32] (for more details see, e.g., [8,19,22]) and complement [4,Corollary 6]. …”

Popoviciu Type Equations on Cylinders

“…The solutions of (19) in a more general setting have been considered in [11] (see also [12]). Various aspects of stability problem for (19) have been studied in [8][9][10].…”