Remarks on the Conditional Quadratic and the Conditional D’Alembert Functional Equations on Particular Normed Spaces
Joint Authors
Fochi, Margherita
Viola, Gabriella
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-06-27
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
Let X be a real normed space with dimension greater than 2 and let f be a real functional defined on X.
Applying some ideas from the studies made on the conditional Cauchy functional equation on the restricted domain of the vectors of equal norm and the isosceles orthogonal vectors, the conditional quadratic equation and the D’Alembert one, namely, ∥x∥=∥y∥⇒f(x+y)+f(x−y)=2f(x)+2f(y) and ∥x∥=∥y∥⇒f(x+y)+f(x−y)=2f(x)f(y), have been studied in this paper, in order to describe their solutions.
Particular normed spaces are introduced for this aim.
American Psychological Association (APA)
Fochi, Margherita& Viola, Gabriella. 2013. Remarks on the Conditional Quadratic and the Conditional D’Alembert Functional Equations on Particular Normed Spaces. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-505579
Modern Language Association (MLA)
Fochi, Margherita& Viola, Gabriella. Remarks on the Conditional Quadratic and the Conditional D’Alembert Functional Equations on Particular Normed Spaces. Abstract and Applied Analysis No. 2013 (2013), pp.1-6.
https://search.emarefa.net/detail/BIM-505579
American Medical Association (AMA)
Fochi, Margherita& Viola, Gabriella. Remarks on the Conditional Quadratic and the Conditional D’Alembert Functional Equations on Particular Normed Spaces. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-505579
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-505579