Set valued functions in Fréchet spaces: Continuity, Hukuhara differentiability and applications to set differential equations
The set K c ( F ) of compact convex subsets of a Fréchet space F is studied in detail and is realized as a projective limit of metric spaces. The notion of Hausdorff metric on it is replaced by a family of corresponding “semi-metrics” which provide the necessary background for the support of continu...
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| Veröffentlicht in: | Nonlinear analysis 2005-05, Vol.61 (4), p.559-575 |
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| creator | Galanis, G.N. Bhaskar, T. Gnana Lakshmikantham, V. Palamides, P.K. |
| description | The set
K
c
(
F
)
of compact convex subsets of a Fréchet space
F
is studied in detail and is realized as a projective limit of metric spaces. The notion of Hausdorff metric on it is replaced by a family of corresponding “semi-metrics” which provide the necessary background for the support of continuity and Lipschitz continuity. Finally the notion of Hukuhara derivative suited to our study is developed. The proposed approach forms the appropriate environment within which the study of set differential equations for Fréchet spaces can be developed. A first example on
R
∞
is included. |
| doi_str_mv | 10.1016/j.na.2005.01.004 |
| format | Article |
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K
c
(
F
)
of compact convex subsets of a Fréchet space
F
is studied in detail and is realized as a projective limit of metric spaces. The notion of Hausdorff metric on it is replaced by a family of corresponding “semi-metrics” which provide the necessary background for the support of continuity and Lipschitz continuity. Finally the notion of Hukuhara derivative suited to our study is developed. The proposed approach forms the appropriate environment within which the study of set differential equations for Fréchet spaces can be developed. A first example on
R
∞
is included.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2005.01.004</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Exact sciences and technology ; Fréchet spaces ; Global analysis, analysis on manifolds ; Hukuhara differentiability ; Mathematics ; Sciences and techniques of general use ; Set differential equations ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Nonlinear analysis, 2005-05, Vol.61 (4), p.559-575</ispartof><rights>2005 Elsevier Ltd</rights><rights>2005 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-4c418980d5932caa1e491bd7924aa9762560fd80ecb8892ae072f10e71bdaf833</citedby><cites>FETCH-LOGICAL-c355t-4c418980d5932caa1e491bd7924aa9762560fd80ecb8892ae072f10e71bdaf833</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0362546X05000155$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16616422$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Galanis, G.N.</creatorcontrib><creatorcontrib>Bhaskar, T. Gnana</creatorcontrib><creatorcontrib>Lakshmikantham, V.</creatorcontrib><creatorcontrib>Palamides, P.K.</creatorcontrib><title>Set valued functions in Fréchet spaces: Continuity, Hukuhara differentiability and applications to set differential equations</title><title>Nonlinear analysis</title><description>The set
K
c
(
F
)
of compact convex subsets of a Fréchet space
F
is studied in detail and is realized as a projective limit of metric spaces. The notion of Hausdorff metric on it is replaced by a family of corresponding “semi-metrics” which provide the necessary background for the support of continuity and Lipschitz continuity. Finally the notion of Hukuhara derivative suited to our study is developed. The proposed approach forms the appropriate environment within which the study of set differential equations for Fréchet spaces can be developed. A first example on
R
∞
is included.</description><subject>Exact sciences and technology</subject><subject>Fréchet spaces</subject><subject>Global analysis, analysis on manifolds</subject><subject>Hukuhara differentiability</subject><subject>Mathematics</subject><subject>Sciences and techniques of general use</subject><subject>Set differential equations</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><recordid>eNp1kM1q3TAQRkVpILdJ91lq065qdyRbsp1dueQPAlkkge7EXHlEdOvIjmQHsun79Dn6YlVwoN10NYtz5hvmY-xEQClA6K_7MmApAVQJogSo37GNaJuqUFKo92wDlZaFqvX3Q_YhpT0AiKbSG_bzlmb-jMNCPXdLsLMfQ-I-8PP4-5d9yDBNaCmd8u0YZh8WP7984ZfLj-UBI_LeO0eRMsGdHzLjGHqO0zR4i2vWPPKUY_4xB05Py0qP2YHDIdHHt3nE7s_P7raXxfXNxdX223VhK6Xmora1aLsWetVV0iIKqjux65tO1ohdo6XS4PoWyO7atpNI0EgngJosoWur6oh9XnOnOD4tlGbz6JOlYcBA45KM7LRSQjVZhFW0cUwpkjNT9I8YX4wA81q02ZuA5rVoA8LkovPKp7dsTBYHFzFYn_7uaS10LWX2TleP8qPPnqJJ1lOw1PtIdjb96P9_5A_K45Vo</recordid><startdate>20050515</startdate><enddate>20050515</enddate><creator>Galanis, G.N.</creator><creator>Bhaskar, T. Gnana</creator><creator>Lakshmikantham, V.</creator><creator>Palamides, P.K.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20050515</creationdate><title>Set valued functions in Fréchet spaces: Continuity, Hukuhara differentiability and applications to set differential equations</title><author>Galanis, G.N. ; Bhaskar, T. Gnana ; Lakshmikantham, V. ; Palamides, P.K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-4c418980d5932caa1e491bd7924aa9762560fd80ecb8892ae072f10e71bdaf833</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Exact sciences and technology</topic><topic>Fréchet spaces</topic><topic>Global analysis, analysis on manifolds</topic><topic>Hukuhara differentiability</topic><topic>Mathematics</topic><topic>Sciences and techniques of general use</topic><topic>Set differential equations</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Galanis, G.N.</creatorcontrib><creatorcontrib>Bhaskar, T. Gnana</creatorcontrib><creatorcontrib>Lakshmikantham, V.</creatorcontrib><creatorcontrib>Palamides, P.K.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Galanis, G.N.</au><au>Bhaskar, T. Gnana</au><au>Lakshmikantham, V.</au><au>Palamides, P.K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Set valued functions in Fréchet spaces: Continuity, Hukuhara differentiability and applications to set differential equations</atitle><jtitle>Nonlinear analysis</jtitle><date>2005-05-15</date><risdate>2005</risdate><volume>61</volume><issue>4</issue><spage>559</spage><epage>575</epage><pages>559-575</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>The set
K
c
(
F
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of compact convex subsets of a Fréchet space
F
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R
∞
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| ispartof | Nonlinear analysis, 2005-05, Vol.61 (4), p.559-575 |
| issn | 0362-546X 1873-5215 |
| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Exact sciences and technology Fréchet spaces Global analysis, analysis on manifolds Hukuhara differentiability Mathematics Sciences and techniques of general use Set differential equations Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Set valued functions in Fréchet spaces: Continuity, Hukuhara differentiability and applications to set differential equations |
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