000 | 03317nam a22004935i 4500 | ||
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001 | 978-1-4020-6919-2 | ||
003 | DE-He213 | ||
005 | 20190213151647.0 | ||
007 | cr nn 008mamaa | ||
008 | 100301s2008 ne | s |||| 0|eng d | ||
020 |
_a9781402069192 _9978-1-4020-6919-2 |
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024 | 7 |
_a10.1007/978-1-4020-6919-2 _2doi |
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050 | 4 | _aQA319-329.9 | |
072 | 7 |
_aPBKF _2bicssc |
|
072 | 7 |
_aMAT037000 _2bisacsh |
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072 | 7 |
_aPBKF _2thema |
|
082 | 0 | 4 |
_a515.7 _223 |
100 | 1 |
_aSimons, Stephen. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
245 | 1 | 0 |
_aFrom Hahn-Banach to Monotonicity _h[electronic resource] / _cby Stephen Simons. |
264 | 1 |
_aDordrecht : _bSpringer Netherlands, _c2008. |
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300 |
_aXIV, 248 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
||
490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 |
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505 | 0 | _aThe Hahn-Banach-Lagrange theorem and some consequences -- Fenchel duality -- Multifunctions, SSD spaces, monotonicity and Fitzpatrick functions -- Monotone multifunctions on general Banach spaces -- Monotone multifunctions on reflexive Banach spaces -- Special maximally monotone multifunctions -- The sum problem for general Banach spaces -- Open problems -- Glossary of classes of multifunctions -- A selection of results. | |
520 | _aIn this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a “big convexification” of the graph of the multifunction and the “minimax technique”for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the Hahn-Banach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach space. | ||
650 | 0 | _aFunctional analysis. | |
650 | 0 | _aMathematical optimization. | |
650 | 0 | _aOperator theory. | |
650 | 1 | 4 |
_aFunctional Analysis. _0http://scigraph.springernature.com/things/product-market-codes/M12066 |
650 | 2 | 4 |
_aCalculus of Variations and Optimal Control; Optimization. _0http://scigraph.springernature.com/things/product-market-codes/M26016 |
650 | 2 | 4 |
_aOperator Theory. _0http://scigraph.springernature.com/things/product-market-codes/M12139 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9789048116454 |
776 | 0 | 8 |
_iPrinted edition: _z9781402069185 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-1-4020-6919-2 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
999 |
_c11447 _d11447 |