On an n-dimensional mixed type additive and quadratic functional equation

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

“…(1) in Banach spaces) to Ulam's question was given by Hyers (see [24]). After his result a great number of papers (see for instance [7,8,[11][12][13][14]21,26,27,29,30] and the references given there) on the subject has been published, generalizing Ulam's problem and Hyers's theorem in various directions and to other (not only functional, see for example [4,37]) equations.…”

On approximate isometries and application to stability of a functional equation

“…We refer to the survey [28] and the celebrated book [18] for this topic and related matters. Some of the latest developments of the stability of functional equations can be found in the papers [2,[4][5][6]15,[19][20][21]25].…”

A General Theorem on the Stability of a Class of Functional Equations including Quartic-Cubic-Quadratic-Additive Equations

“…Till now, we have followed out a routine and monotonous procedure for studying the stability problems of the quartic-cubic-quadratic-additive functional equations. However, the stability theorems of this paper can save us much trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations (see [8,9,10,12,13]).…”