LEADER 03654nam 22005895 450 001 9910254072203321 005 20200702165500.0 010 $a3-319-27978-5 024 7 $a10.1007/978-3-319-27978-7 035 $a(CKB)3710000000717740 035 $a(DE-He213)978-3-319-27978-7 035 $a(MiAaPQ)EBC6310731 035 $a(MiAaPQ)EBC5587959 035 $a(Au-PeEL)EBL5587959 035 $a(OCoLC)951214711 035 $a(PPN)194077225 035 $a(EXLCZ)993710000000717740 100 $a20160523d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Fixed-Point Farrago /$fby Joel H. Shapiro 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XIV, 221 p. 8 illus.) 225 1 $aUniversitext,$x0172-5939 311 $a3-319-27976-9 320 $aIncludes bibliographical references and index. 327 $a1. From Newton to Google -- 2. Brouwer in Dimension Two -- 3. Contraction Mappings -- 4. Brouwer in Higher Dimensions -- 5. Nash Equilibrium -- 6. Nash's "one-page proof" -- 7. The Schauder Fixed-Point Theorem -- 8. The Invariant Subspace Problem -- 9. The Markov?Kakutani Theorem -- 10. The Meaning of Means -- 11. Paradoxical Decompositions -- 12. Fixed Points for Non-commuting Map Families -- 13. Beyond Markov?Kakutani -- A. Advanced Calculus -- B. Compact Metric Spaces -- C. Convex Sets and Normed Spaces -- D. Euclidean Isometries -- E. A Little Group Theory, a Little Set Theory -- References -- Index -- List of Symbols. 330 $aThis text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of undergraduate proficiency to graduate-level sophistication. Appendices provide an introduction to (or refresher on) some of the prerequisite material and exercises are integrated into the text, contributing to the volume?s ability to be used as a self-contained text. Readers will find the presentation especially useful for independent study or as a supplement to a graduate course in fixed-point theory. The material is split into four parts: the first introduces the Banach Contraction-Mapping Principle and the Brouwer Fixed-Point Theorem, along with a selection of interesting applications; the second focuses on Brouwer?s theorem and its application to John Nash?s work; the third applies Brouwer?s theorem to spaces of infinite dimension; and the fourth rests on the work of Markov, Kakutani, and Ryll?Nardzewski surrounding fixed points for families of affine maps. 410 0$aUniversitext,$x0172-5939 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aNumerical analysis 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aNumerical analysis. 615 14$aAnalysis. 615 24$aNumerical Analysis. 676 $a515.7248 700 $aShapiro$b Joel H$4aut$4http://id.loc.gov/vocabulary/relators/aut$060142 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254072203321 996 $aFixed-point Farrago$91523051 997 $aUNINA