Generalized dissipativeness in a Banach space
Suppose X is a real or complex Banach space with dual X* and a semiscalar product [,]. For k a real number, a subset B of X×X will be called k-dissipative if for each pair of elements (x1,y1), (x2,y2) in B, there existsh∈{f∈X*:[x,f]=|x|2=|f|2}such thatRe[y1−y2,h]≤k|x1−x2|2.This definition extends a...
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| Language: | English |
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Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171296000051 |
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| _version_ | 1832562132378451968 |
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| author | David R. Gurney |
| author_facet | David R. Gurney |
| author_sort | David R. Gurney |
| collection | DOAJ |
| description | Suppose X is a real or complex Banach space with dual X* and a semiscalar product [,]. For k a real number, a subset B of X×X will be called k-dissipative if for each pair of elements (x1,y1), (x2,y2) in B, there existsh∈{f∈X*:[x,f]=|x|2=|f|2}such thatRe[y1−y2,h]≤k|x1−x2|2.This definition extends a notion of dissipativeness which is equivalent to having k equal zero here. A number of definitions and theorems related to this original dissipative notion are generalized in the present paper to fit the k-dissipative situation, and proofs are given for the new theorems. |
| format | Article |
| id | doaj-art-d5e55e64f60445a3b8c72f5936fb2369 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d5e55e64f60445a3b8c72f5936fb23692025-02-03T01:23:20ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-01191253210.1155/S0161171296000051Generalized dissipativeness in a Banach spaceDavid R. Gurney0Southeastern Louisiana University, SLU 541, Hammond, LA 70402, USASuppose X is a real or complex Banach space with dual X* and a semiscalar product [,]. For k a real number, a subset B of X×X will be called k-dissipative if for each pair of elements (x1,y1), (x2,y2) in B, there existsh∈{f∈X*:[x,f]=|x|2=|f|2}such thatRe[y1−y2,h]≤k|x1−x2|2.This definition extends a notion of dissipativeness which is equivalent to having k equal zero here. A number of definitions and theorems related to this original dissipative notion are generalized in the present paper to fit the k-dissipative situation, and proofs are given for the new theorems.http://dx.doi.org/10.1155/S0161171296000051dissipativehyperdissipativesemi-scalar productBanach spacemulti-valued mappingscontraction semi-groups. |
| spellingShingle | David R. Gurney Generalized dissipativeness in a Banach space International Journal of Mathematics and Mathematical Sciences dissipative hyperdissipative semi-scalar product Banach space multi-valued mappings contraction semi-groups. |
| title | Generalized dissipativeness in a Banach space |
| title_full | Generalized dissipativeness in a Banach space |
| title_fullStr | Generalized dissipativeness in a Banach space |
| title_full_unstemmed | Generalized dissipativeness in a Banach space |
| title_short | Generalized dissipativeness in a Banach space |
| title_sort | generalized dissipativeness in a banach space |
| topic | dissipative hyperdissipative semi-scalar product Banach space multi-valued mappings contraction semi-groups. |
| url | http://dx.doi.org/10.1155/S0161171296000051 |
| work_keys_str_mv | AT davidrgurney generalizeddissipativenessinabanachspace |