Ulam stability of functional equations in 2-Banach spaces via the fixed point method

Abstract

Using the fixed point method, we prove the Ulam stability of two general functional equations in several variables in 2-Banach spaces. As corollaries from our main results, some outcomes on the stability of a few known equations being special cases of the considered ones will be presented. In particular, we extend several recent results on the Ulam stability of functional equations in 2-Banach spaces.

Stability of a General Functional Equation in m-Banach Spaces

“…Its stability was studied in [9,11,17], and our result complements and generalizes the corresponding outcomes obtained in these two papers.…”

“…( 3) is Ulam stable in m-Banach spaces. This complements some results from [11] as well as generalizes those from [9]. Moreover, as corollaries from our main result, we get several outcomes on approximate solutions of a few known functional equations being special cases of (3).…”

“…This equation was recently introduced and investigated in [9,11] as a natural generalization of (2) (it is obvious that (3) with a 1,i 1 ,...,i n = . .…”

“…Moreover, as corollaries from our main result, we get several outcomes on approximate solutions of a few known functional equations being special cases of (3). Let us finally mention that in papers [9,11] a variant of the fixed point method is applied, while we use another technique: the direct/Hyers method.…”

“…which was introduced and studied in [25] (see also [9] for a stability result in 2-Banach spaces). Using Theorem 2 with n…”