Hyers–Ulam–Rassias Stability of a Quadratic and Additive Functional Equation in Quasi-Banach Spaces

Abstract

In this paper we establish the general solution of the functional equation (y) and investigate the Hyers-Ulam-Rassias stability of this equation in quasiBanach spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in

Solution and stability of a mixed type functional equation

“…in quasi Banach Space was dealt by Moradlou et al,in [15]. It is easy to see that the function f (x) = ax 2 + bx is a solution of the functional equation (1.3); for the general case of (1.3) see [5] and [6].…”

Solution and Stability of a General Mixed Type Cubic and Quartic Functional Equation

“…In [16], the authors obtained the general solution and the generalized Hyers-Ulam-Rassias stability of (6) in quasi-Banach space. The literature on the stability of the mixed type functional equations is very rich; see [17][18][19][20][21][22]. In the present paper, we extend (6) and consider the following functional equation…”

Generalized Hyers Ulam Stability of an Aqcq-Functional Equation in Non-Archimedean Banach Spaces

“…The stability problems of several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem (see [4], [8], [11], [13], [14], [16], [20]- [35]). …”