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001 978-1-4020-6919-2
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007 cr nn 008mamaa
008 100301s2008 ne | s |||| 0|eng d
020 _a9781402069192
_9978-1-4020-6919-2
024 7 _a10.1007/978-1-4020-6919-2
_2doi
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
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.
300 _aXIV, 248 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434
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