Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces

<p>Abstract</p> <p>Lex <it>X </it>be a normed space and <it>Y </it>be a Banach fuzzy space. Let <it>D </it>= {(<it>x</it>, <it>y</it>) ∈ <it>X </it>× <it>X </it>: ||<it>x<...

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Main Authors:	Kang Jung Im, Cho Yeol Je, Najati Abbas
Format:	Article
Language:	English
Published:	SpringerOpen 2011-01-01
Series:	Journal of Inequalities and Applications
Subjects:	Pexiderized Cauchy functional equation generalized Hyers-Ulam stability Jensen functional equation non-Archimedean space
Online Access:	http://www.journalofinequalitiesandapplications.com/content/2011/1/78

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spelling	doaj-1edc00ec5a154fc5bc28cc49aeda90062020-11-24T23:05:19ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2011-01-012011178Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spacesKang Jung ImCho Yeol JeNajati Abbas<p>Abstract</p> <p>Lex <it>X </it>be a normed space and <it>Y </it>be a Banach fuzzy space. Let <it>D </it>= {(<it>x</it>, <it>y</it>) ∈ <it>X </it>× <it>X </it>: \|\|<it>x</it>\|\| + \|\|<it>y</it>\|\| ≥ <it>d</it>} where <it>d </it>> 0. We prove that the Pexiderized Jensen functional equation is stable in the fuzzy norm for functions defined on <it>D </it>and taking values in <it>Y</it>. We consider also the Pexiderized Cauchy functional equation.</p> <p> <b>2000 Mathematics Subject Classification: </b>39B22; 39B82; 46S10.</p> http://www.journalofinequalitiesandapplications.com/content/2011/1/78Pexiderized Cauchy functional equationgeneralized Hyers-Ulam stabilityJensen functional equationnon-Archimedean space
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Kang Jung Im Cho Yeol Je Najati Abbas
spellingShingle	Kang Jung Im Cho Yeol Je Najati Abbas Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces Journal of Inequalities and Applications Pexiderized Cauchy functional equation generalized Hyers-Ulam stability Jensen functional equation non-Archimedean space
author_facet	Kang Jung Im Cho Yeol Je Najati Abbas
author_sort	Kang Jung Im
title	Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces
title_short	Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces
title_full	Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces
title_fullStr	Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces
title_full_unstemmed	Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces
title_sort	local stability of the pexiderized cauchy and jensen's equations in fuzzy spaces
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1025-5834 1029-242X
publishDate	2011-01-01
description	<p>Abstract</p> <p>Lex <it>X </it>be a normed space and <it>Y </it>be a Banach fuzzy space. Let <it>D </it>= {(<it>x</it>, <it>y</it>) ∈ <it>X </it>× <it>X </it>: \|\|<it>x</it>\|\| + \|\|<it>y</it>\|\| ≥ <it>d</it>} where <it>d </it>> 0. We prove that the Pexiderized Jensen functional equation is stable in the fuzzy norm for functions defined on <it>D </it>and taking values in <it>Y</it>. We consider also the Pexiderized Cauchy functional equation.</p> <p> <b>2000 Mathematics Subject Classification: </b>39B22; 39B82; 46S10.</p>
topic	Pexiderized Cauchy functional equation generalized Hyers-Ulam stability Jensen functional equation non-Archimedean space
url	http://www.journalofinequalitiesandapplications.com/content/2011/1/78
work_keys_str_mv	AT kangjungim localstabilityofthepexiderizedcauchyandjensensequationsinfuzzyspaces AT choyeolje localstabilityofthepexiderizedcauchyandjensensequationsinfuzzyspaces AT najatiabbas localstabilityofthepexiderizedcauchyandjensensequationsinfuzzyspaces
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Local stability of the Pexiderized Cauchy and Jensen's equations in fuzzy spaces

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