Elementary remarks on Ulam–Hyers stability of linear functional equations

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In this paper the general method for proving stability of linear functional equations is described.

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On a direct method for proving the Hyers–Ulam stability of functional equations (2010, background): “Forti gave quite a general approach (see also [4,6]) from which we can derive many stability results without repeating all the time the same procedure.”
Hyperstability of the Cauchy equation on restricted domains (2013, background): “2 corresponds to some observations in [18,19,40], but actually is based on a fixed point theorem in [7, Theorem 1] (see also [8, Theorem 2]).”
On Ulam’s Type Stability of the Linear Equation and Related Issues (2014, background): “Let us yet mention that the equation plays a significant role in the investigations of stability of the functional equations in several variables; for suitable examples, we refer the reader, for example, to [8, 27–31].”