LEADER 03995nam 22005055 450 001 9910309662203321 005 20200703062639.0 010 $a981-13-3158-8 024 7 $a10.1007/978-981-13-3158-9 035 $a(CKB)4100000007463635 035 $a(DE-He213)978-981-13-3158-9 035 $a(MiAaPQ)EBC6310726 035 $a(PPN)233797211 035 $a(EXLCZ)994100000007463635 100 $a20190110d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aElementary Fixed Point Theorems /$fby P.V. Subrahmanyam 205 $a1st ed. 2018. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2018. 215 $a1 online resource (XIII, 302 p. 5 illus.) 225 1 $aForum for Interdisciplinary Mathematics,$x2364-6748 311 $a981-13-3157-X 320 $aIncludes bibliographical references. 327 $aChapter 1. Prerequisites -- Chapter 2. Fixed Points of Some Real and Complex Functions -- Chapter 3. Fixed Points and Order -- Chapter 4. Partially Ordered Topological Spaces and Fixed Points -- Chapter 5. Contraction Principle -- Chapter 6. Applications of the Contraction Principle -- Chapter 7. Caristi?s ?xed point theorem -- Chapter 8. Contractive and Nonexpansive Mappings -- Chapter 9. Geometric Aspects of Banach Spaces and Nonexpansive Mappings -- Chapter 10. Brouwer?s Fixed Point Theorem -- Chapter 11. Schauder?s Fixed Point Theorem and Allied Theorems -- Chapter 12. Basic Analytic Degree Theory af a Mapping. 330 $aThis book provides a primary resource in basic fixed-point theorems due to Banach, Brouwer, Schauder and Tarski and their applications. Key topics covered include Sharkovsky?s theorem on periodic points, Thron?s results on the convergence of certain real iterates, Shield?s common fixed theorem for a commuting family of analytic functions and Bergweiler?s existence theorem on fixed points of the composition of certain meromorphic functions with transcendental entire functions. Generalizations of Tarski?s theorem by Merrifield and Stein and Abian?s proof of the equivalence of Bourbaki?Zermelo fixed-point theorem and the Axiom of Choice are described in the setting of posets. A detailed treatment of Ward?s theory of partially ordered topological spaces culminates in Sherrer fixed-point theorem. It elaborates Manka?s proof of the fixed-point property of arcwise connected hereditarily unicoherent continua, based on the connection he observed between set theory and fixed-point theory via a certain partial order. Contraction principle is provided with two proofs: one due to Palais and the other due to Barranga. Applications of the contraction principle include the proofs of algebraic Weierstrass preparation theorem, a Cauchy?Kowalevsky theorem for partial differential equations and the central limit theorem. It also provides a proof of the converse of the contraction principle due to Jachymski, a proof of fixed point theorem for continuous generalized contractions, a proof of Browder?Gohde?Kirk fixed point theorem, a proof of Stalling's generalization of Brouwer's theorem, examine Caristi's fixed point theorem, and highlights Kakutani's theorems on common fixed points and their applications. 410 0$aForum for Interdisciplinary Mathematics,$x2364-6748 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aAnalysis. 676 $a515.7248 700 $aSubrahmanyam$b P.V$4aut$4http://id.loc.gov/vocabulary/relators/aut$0906909 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910309662203321 996 $aElementary Fixed Point Theorems$92028738 997 $aUNINA