INNER PRODUCT SPACES AND FUNCTIONAL EQUATIONS

Cho, YJ; Park, C; Rassias, TM; Saadati, R

dc.contributor.author	Cho, YJ	en
dc.contributor.author	Park, C	en
dc.contributor.author	Rassias, TM	en
dc.contributor.author	Saadati, R	en
dc.date.accessioned	2014-03-01T02:04:30Z
dc.date.available	2014-03-01T02:04:30Z
dc.date.issued	2011	en
dc.identifier.issn	1521-1398	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29449
dc.subject	additive mapping	en
dc.subject	quadratic mapping	en
dc.subject	functional equation associated with inner product space	en
dc.subject	generalized Hyers-Ulam stability	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	BANACH-SPACES	en
dc.subject.other	STABILITY	en
dc.subject.other	MAPPINGS	en
dc.subject.other	ULAM	en
dc.title	INNER PRODUCT SPACES AND FUNCTIONAL EQUATIONS	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	In [7], Th.M. Rassias introduced the following equality Sigma(n)(i,j=1) parallel to x(i) - x(j)parallel to(2) = 2n Sigma(n)(i=1) parallel to x(i)parallel to(2), Sigma(n)(i=1) x(i)=0 for a fixed integer n >= 3. Let V IV be real vector spaces. In this paper, we show that, if a mapping f : V -> W satisfies Sigma(n)(i,j=1) f(x(i) - x(j)) = 2n Sigma(n)(i=1) f(x(i)) for all x(1), ... , x(n) is an element of V with Sigma(n)(i=1) x(i)=0, then the mapping f: V -> W is realized as the sum of an additive mapping and a quadratic mapping. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.1) in real Banach spaces.	en
heal.publisher	EUDOXUS PRESS, LLC	en
heal.journalName	JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS	en
dc.identifier.isi	ISI:000288575900009	en
dc.identifier.volume	13	en
dc.identifier.issue	2	en
dc.identifier.spage	296	en
dc.identifier.epage	304	en