LEADER 03841nam 22006855 450 001 9910484720603321 005 20200702074711.0 010 $a9781402069192 010 $a1402069197 024 7 $a10.1007/978-1-4020-6919-2 035 $a(CKB)1000000000437319 035 $a(SSID)ssj0000317793 035 $a(PQKBManifestationID)11211509 035 $a(PQKBTitleCode)TC0000317793 035 $a(PQKBWorkID)10294521 035 $a(PQKB)10292087 035 $a(DE-He213)978-1-4020-6919-2 035 $a(MiAaPQ)EBC3062878 035 $a(MiAaPQ)EBC6281040 035 $a(PPN)123741343 035 $a(EXLCZ)991000000000437319 100 $a20100301d2008 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aFrom Hahn-Banach to Monotonicity /$fby Stephen Simons 205 $a2nd ed. 2008. 210 1$aDordrecht :$cSpringer Netherlands :$cImprint: Springer,$d2008. 215 $a1 online resource (XIV, 248 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 300 $aOriginal edition published as: Minimax and monotonicity. 311 08$a9781402069185 311 08$a1402069189 320 $aIncludes bibliographical references (pages [233]-238) and index. 327 $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. 330 $aIn this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a ?big convexification? of the graph of the multifunction and the ?minimax technique?for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the Hahn-Banach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach space. 410 0$aLecture Notes in Mathematics,$x0075-8434 606 $aFunctional analysis 606 $aCalculus of variations 606 $aOperator theory 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 615 0$aFunctional analysis. 615 0$aCalculus of variations. 615 0$aOperator theory. 615 14$aFunctional Analysis. 615 24$aCalculus of Variations and Optimal Control; Optimization. 615 24$aOperator Theory. 676 $a515.7248 700 $aSimons$b Stephen$4aut$4http://id.loc.gov/vocabulary/relators/aut$057289 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484720603321 996 $aFrom Hahn-Banach to monotonicity$9230764 997 $aUNINA