The generalized hyperstability of general linear equations in quasi-Banach spaces

Investigations on the Hyers–Ulam stability of generalized radical functional equations

“…for x ∈ G and i = 1, 2. Thus, by (19) and 20 Then, according to Remarks 3 and 4, d is a dq-2 p−1 -metric in R. For such d conditions (13) and (14) take the form…”

“…Let us mention yet, that a function d : X 2 → R + such that (a), (b) and (II) are valid, have been called a b-metric (cf., e.g., [13]). That term has been used for the first time in [9] with K = 2 and next in [10] for any K ≥ 1.…”

A fixed point approach to the hyperstability of the general linear equation in β-Banach spaces

“…However, it seems that the term hyperstability was used for the Ąrst time in [33] (quite often it is confused with superstability, which admits also bounded functions). There are many researchers investigating the hyperstability results for functional equations in many areas (see, e.g., [8,9,16,21,26]).…”

Stability of the Fréchet Equation in Quasi-Banach Spaces

“…By using that fixed point theorem, they obtained a hyperstability of general linear equations. For more information on the stability of functional equations and fixed point theorems, we refer to [25,26].Several authors have studied the stability of many functional equations in quasi-Banach spaces (see, e.g., [24,[27][28][29][30][31][32]). The purpose of this paper is to obtain the (hyper)stability of (2) by using the fixed point theorem of Dung and Hang [24].…”

“…Several authors have studied the stability of many functional equations in quasi-Banach spaces (see, e.g., [24,[27][28][29][30][31][32]).…”