The Product Formula and Evolution Families of Nonexpansive Mappings
In this work we obtain a product formula type for a two-parameters commuting family of nonexpansive mappings on D . This is established by following the techniques used by Simeon Reich and David Shoikhet in the study of one-parameter semigroups of holomorphic and nonexpansive self-mappings in D . Al...
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| Veröffentlicht in: | Boletim da Sociedade Brasileira de Matemática 2019-09, Vol.50 (3), p.625-644 |
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| creator | Benítez-Babilonia, Luis López, Nancy Felipe, Raúl |
| description | In this work we obtain a product formula type for a two-parameters commuting family of nonexpansive mappings on
D
. This is established by following the techniques used by Simeon Reich and David Shoikhet in the study of one-parameter semigroups of holomorphic and nonexpansive self-mappings in
D
. Also, we stablish such a formula for the family of non-linear resolvent of a strongly
ρ
-monotone functions on
D
and its relation with evolution families of nonexpansive mappings on
D
. It is worthy mentioning that the product formula is linked with semigroup of linear and nonlinear operators. Also it is associated with the study of vector fields and flows, but in the literature it is established a product formula for time independent flow. |
| doi_str_mv | 10.1007/s00574-018-0118-4 |
| format | Article |
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D
. This is established by following the techniques used by Simeon Reich and David Shoikhet in the study of one-parameter semigroups of holomorphic and nonexpansive self-mappings in
D
. Also, we stablish such a formula for the family of non-linear resolvent of a strongly
ρ
-monotone functions on
D
and its relation with evolution families of nonexpansive mappings on
D
. It is worthy mentioning that the product formula is linked with semigroup of linear and nonlinear operators. Also it is associated with the study of vector fields and flows, but in the literature it is established a product formula for time independent flow.</description><identifier>ISSN: 1678-7544</identifier><identifier>EISSN: 1678-7714</identifier><identifier>DOI: 10.1007/s00574-018-0118-4</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Evolution ; Fields (mathematics) ; Labeling ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Monotone functions ; Operators (mathematics) ; Parameters ; Theoretical</subject><ispartof>Boletim da Sociedade Brasileira de Matemática, 2019-09, Vol.50 (3), p.625-644</ispartof><rights>Sociedade Brasileira de Matemática 2018</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-7c42bdd436ed900caf78e980bd7429c377853e76faf96b019c160f4059020b1f3</citedby><cites>FETCH-LOGICAL-c316t-7c42bdd436ed900caf78e980bd7429c377853e76faf96b019c160f4059020b1f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00574-018-0118-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00574-018-0118-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Benítez-Babilonia, Luis</creatorcontrib><creatorcontrib>López, Nancy</creatorcontrib><creatorcontrib>Felipe, Raúl</creatorcontrib><title>The Product Formula and Evolution Families of Nonexpansive Mappings</title><title>Boletim da Sociedade Brasileira de Matemática</title><addtitle>Bull Braz Math Soc, New Series</addtitle><description>In this work we obtain a product formula type for a two-parameters commuting family of nonexpansive mappings on
D
. This is established by following the techniques used by Simeon Reich and David Shoikhet in the study of one-parameter semigroups of holomorphic and nonexpansive self-mappings in
D
. Also, we stablish such a formula for the family of non-linear resolvent of a strongly
ρ
-monotone functions on
D
and its relation with evolution families of nonexpansive mappings on
D
. It is worthy mentioning that the product formula is linked with semigroup of linear and nonlinear operators. Also it is associated with the study of vector fields and flows, but in the literature it is established a product formula for time independent flow.</description><subject>Evolution</subject><subject>Fields (mathematics)</subject><subject>Labeling</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Monotone functions</subject><subject>Operators (mathematics)</subject><subject>Parameters</subject><subject>Theoretical</subject><issn>1678-7544</issn><issn>1678-7714</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kLtOwzAUhi0EEuXyAGyWmAPHjmPHI6paQCqXocyW49glVRoHO6ng7XEVEBPDuQz_RfoQuiJwQwDEbQQoBMuAlGnSYkdoRrgoMyEIO_79C8ZO0VmMWwDgRZHP0Hz9bvFr8PVoBrz0YTe2Guuuxou9b8eh8R1e6l3TNjZi7_Cz7-xnr7vY7C1-0n3fdJt4gU6cbqO9_Lnn6G25WM8fstXL_eP8bpWZnPAhE4bRqq5Zzm0tAYx2orSyhKoWjEqTC1EWuRXcaSd5BUQawsExKCRQqIjLz9H1lNsH_zHaOKitH0OXKhWlggpOKZVJRSaVCT7GYJ3qQ7PT4UsRUAdWamKlEit1YKVY8tDJE5O229jwl_y_6RvhV2sD</recordid><startdate>20190910</startdate><enddate>20190910</enddate><creator>Benítez-Babilonia, Luis</creator><creator>López, Nancy</creator><creator>Felipe, Raúl</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190910</creationdate><title>The Product Formula and Evolution Families of Nonexpansive Mappings</title><author>Benítez-Babilonia, Luis ; López, Nancy ; Felipe, Raúl</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-7c42bdd436ed900caf78e980bd7429c377853e76faf96b019c160f4059020b1f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Evolution</topic><topic>Fields (mathematics)</topic><topic>Labeling</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Monotone functions</topic><topic>Operators (mathematics)</topic><topic>Parameters</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Benítez-Babilonia, Luis</creatorcontrib><creatorcontrib>López, Nancy</creatorcontrib><creatorcontrib>Felipe, Raúl</creatorcontrib><collection>CrossRef</collection><jtitle>Boletim da Sociedade Brasileira de Matemática</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Benítez-Babilonia, Luis</au><au>López, Nancy</au><au>Felipe, Raúl</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Product Formula and Evolution Families of Nonexpansive Mappings</atitle><jtitle>Boletim da Sociedade Brasileira de Matemática</jtitle><stitle>Bull Braz Math Soc, New Series</stitle><date>2019-09-10</date><risdate>2019</risdate><volume>50</volume><issue>3</issue><spage>625</spage><epage>644</epage><pages>625-644</pages><issn>1678-7544</issn><eissn>1678-7714</eissn><abstract>In this work we obtain a product formula type for a two-parameters commuting family of nonexpansive mappings on
D
. This is established by following the techniques used by Simeon Reich and David Shoikhet in the study of one-parameter semigroups of holomorphic and nonexpansive self-mappings in
D
. Also, we stablish such a formula for the family of non-linear resolvent of a strongly
ρ
-monotone functions on
D
and its relation with evolution families of nonexpansive mappings on
D
. It is worthy mentioning that the product formula is linked with semigroup of linear and nonlinear operators. Also it is associated with the study of vector fields and flows, but in the literature it is established a product formula for time independent flow.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00574-018-0118-4</doi><tpages>20</tpages></addata></record> |
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| subjects | Evolution Fields (mathematics) Labeling Mathematical and Computational Physics Mathematics Mathematics and Statistics Monotone functions Operators (mathematics) Parameters Theoretical |
| title | The Product Formula and Evolution Families of Nonexpansive Mappings |
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