Treffer: On the Hyers–Ulam–Rassias stability of generalized quadratic mappings in Banach modules: On the Hyers-Ulam-Rassias stability of generalized quadratic mappings in Banach modules.
Title:
On the Hyers–Ulam–Rassias stability of generalized quadratic mappings in Banach modules: On the Hyers-Ulam-Rassias stability of generalized quadratic mappings in Banach modules.
Authors:
Source:
Journal of Mathematical Analysis and Applications. 291:214-223
Publisher Information:
Elsevier BV, 2004.
Publication Year:
2004
Subject Terms:
Banach \(\ast\)-algebra, Banach modules, Applied Mathematics, Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX), Stability, separation, extension, and related topics for functional equations, stability, quadratic functional equation, 01 natural sciences, Generalized A-quadratic mapping, Functional equations for functions with more general domains and/or ranges, generalized \(A\)-quadratic mappings, 0101 mathematics, Stability, Analysis
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
0022-247X
DOI:
10.1016/j.jmaa.2003.10.027
Access URL:
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....bbdf3a6a53a9e6d53b19fd11d2ae9076
Database:
OpenAIRE
Weitere Informationen
Let \(X,Y\) be Banach modules over a Banach \(\ast\)-algebra \(A\). A mapping \(Q:X\to Y\) is called \(A\)-quadratic if it satisfies \[ Q(x+y)+Q(x-y)=2Q(x)+2Q(y)\quad \text{and}\quad Q(ax)=aQ(x)a^{\ast} \] for all \(a\in A\), \(x,y\in X\). Two types of generalized \(A\)-quadratic mappings are considered and for both of them the stability is proved. The research was motivated by the stability results for the quadratic equation obtained by \textit{F. Skof} [Rend. Semin. Mat. Fis. Milano 53, 113--129 (1983; Zbl 0599.39007)], \textit{P. W. Cholewa} [Aequationes Math. 27, 76--86 (1984; Zbl 0549.39006)] and \textit{S. Czerwik} [Abh. Math. Semin. Univ. Hamb. 62, 59--64 (1992; Zbl 0779.39003)] as well as by some ideas of \textit{Th. M. Rassias}.