LEADER 04300nam 22006255 450 001 9910349334603321 005 20220322131113.0 010 $a3-030-19670-4 024 7 $a10.1007/978-3-030-19670-7 035 $a(CKB)4100000009362549 035 $a(DE-He213)978-3-030-19670-7 035 $a(MiAaPQ)EBC5918464 035 $a(PPN)258059788 035 $a(EXLCZ)994100000009362549 100 $a20190618d2019 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFixed Point Theorems and Applications /$fby Vittorino Pata 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XVII, 171 p. 1 illus.) 225 1 $aLa Matematica per il 3+2,$x2038-5722 ;$v116 311 $a3-030-19669-0 327 $a1 The Banach contraction principle 7 -- 2 The Boyd-Wongtheorem 13 -- 3 Further extensions of the contraction principle 16 -- 4 Weak contractions 23 -- 5 Contractions of ?-type 29 -- 6 Sequences of maps and ?xed points 36 -- 7 Fixed points of non-expansive maps 39 -- 8 The Riesz mean ergodic theorem 42 -- 9 The Brouwer ?xed point theorem 46 -- 10 The Schauder-Tychono? ?xed point theorem 50 -- 11 Further consequences of the Schauder-Tychono? theorem 55 -- 12 TheMarkov-Kakutani theorem 60 -- 13 TheKakutani-Ky Fan theorem 62 -- 14 The implicit function theorem 70 -- 15 Location of zeros 75 -- 16 Ordinary di?erential equations in Banach spaces 78 -- 17 The Lax-Milgram lemma 89 -- 18 An abstract elliptic problem 97 -- 19 Semilinear evolution equations 101 -- 20 An abstract parabolic problem 108 -- 21 The invariant subspace problem 114 -- 22 Measure preserving maps on compact Hausdor? spaces 118 -- 23 Invariant means on semigroups 120 -- 24 Haar measures 123 -- 25 Game theory 130 -- 26 Problems. 330 $aThis book addresses fixed point theory, a fascinating and far-reaching field with applications in several areas of mathematics. The content is divided into two main parts. The first, which is more theoretical, develops the main abstract theorems on the existence and uniqueness of fixed points of maps. In turn, the second part focuses on applications, covering a large variety of significant results ranging from ordinary differential equations in Banach spaces, to partial differential equations, operator theory, functional analysis, measure theory, and game theory. A final section containing 50 problems, many of which include helpful hints, rounds out the coverage. Intended for Master?s and PhD students in Mathematics or, more generally, mathematically oriented subjects, the book is designed to be largely self-contained, although some mathematical background is needed: readers should be familiar with measure theory, Banach and Hilbert spaces, locally convex topological vector spaces and, in general, with linear functional analysis. 410 0$aLa Matematica per il 3+2,$x2038-5722 ;$v116 606 $aFunctional analysis 606 $aPartial differential equations 606 $aDifferential equations 606 $aTopology 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000 615 0$aFunctional analysis. 615 0$aPartial differential equations. 615 0$aDifferential equations. 615 0$aTopology. 615 14$aFunctional Analysis. 615 24$aPartial Differential Equations. 615 24$aOrdinary Differential Equations. 615 24$aTopology. 676 $a515.7248 676 $a515.7248 700 $aPata$b Vittorino$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781328 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349334603321 996 $aFixed Point Theorems and Applications$91732468 997 $aUNINA