03639nam 22008415 450 991014630480332120250731082119.03-540-68931-110.1007/BFb0093633(CKB)1000000000437320(SSID)ssj0000324847(PQKBManifestationID)12117822(PQKBTitleCode)TC0000324847(PQKBWorkID)10321908(PQKB)11119411(DE-He213)978-3-540-68931-7(MiAaPQ)EBC5592465(Au-PeEL)EBL5592465(OCoLC)1066198673(MiAaPQ)EBC6842663(Au-PeEL)EBL6842663(OCoLC)159957204(PPN)155217674(BIP)39410033(BIP)47743207(EXLCZ)99100000000043732020121227d1998 u| 0engurnn#008mamaatxtccrMinimax and Monotonicity /by Stephen Simons1st ed. 1998.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1998.1 online resource (XI, 172 p.)Lecture Notes in Mathematics,1617-9692 ;1693Bibliographic Level Mode of Issuance: Monograph3-540-64755-4 Functional analytic preliminaries -- Multifunctions -- A digression into convex analysis -- General monotone multifunctions -- The sum problem for reflexive spaces -- Special maximal monotone multifunctions -- Subdifferentials -- Discontinuous positive linear operators -- The sum problem for general banach spaces -- Open problems.Focussing on the theory (both classical and recent) of monotone multifunctions on a (possibly nonreflexive) Banach space, this book looks at the big convexification of a multifunction; convex functions associated with a multifunction; minimax theorems as a tool in functional analysis and convex analysis. It includes new results on the existence of continuous linear functionals; the conjugates, biconjugates and subdifferentials of convex lower semicontinuous functions, Fenchel duality; (possibly unbounded) positive linear operators from a Banach space into its dual; the sum of maximal monotone operators, and a list of open problems. The reader is expected to know basic functional analysis and calculus of variations, including the Bahn-Banach theorem, Banach-Alaoglu theorem, Ekeland's variational principle.Lecture Notes in Mathematics,1617-9692 ;1693Functional analysisOperator theorySystem theoryControl theoryMathematical optimizationCalculus of variationsFunctional AnalysisOperator TheorySystems Theory, ControlCalculus of Variations and OptimizationFunctional analysis.Operator theory.System theory.Control theory.Mathematical optimization.Calculus of variations.Functional Analysis.Operator Theory.Systems Theory, Control.Calculus of Variations and Optimization.515.724849J35msc47H05mscSimons Stephen1938-57289MiAaPQMiAaPQMiAaPQBOOK9910146304803321Minimax and monotonicity78168UNINA