On the generalized Hyers–Ulam–Rassias stability in Banach modules over a C∗-algebra

Abstract

In this paper, we will investigate the generalized Hyers-Ulam-Rassias stability of an n-dimensional quadratic functional equation in Banach modules over a C * -algebra and unitary elements.  2004 Elsevier Inc. All rights reserved.

A FIXED POINT APPROACH TO THE STABILITY OF QUINTIC MAPPINGS IN QUASI Β-Normed SPACES

“…This theorem was later extended for all p = 1 and this result of Rassias lead mathematicians working in stability of functional equations to establish what is known today as Hyers-Ulam-Rassias stability or Cauchy-Rassias stability as well as to introduce new definitions of stability concepts. During the last three decades, several stability problems of a large variety of functional equations have been extensively studied and generalized by a number of authors [2], [5], [12], [6], [7], [10], [17], [11], [18], [19], and [20]. In particular, Cho and et al [4] introduced the quintic functional equation…”

A Multidimensional Functional Equation Having Quadratic Forms as Solutions

“…Later, many different quadratic functional equations were solved by numerous authors [2][3][4][5][6].…”

On the Fuzzy Stability of Cubic Mappings Using Fixed Point Method

“…The paper [23] has influentially provided in development of what we call the Hyers-Ulam stability or the Hyers-Ulam-Rassias stability of functional equations. Since then the stability problems of several functional equations and various normed spaces have been extensively investigated and generalized by a number of authors [7], [9], [11], [23] and [2].…”