LEADER 03482nam 2200661 450 001 9910485153103321 005 20210218000629.0 010 $a1-280-85350-6 010 $a9786610853502 010 $a3-540-72234-3 024 7 $a10.1007/978-3-540-72234-2 035 $a(CKB)1000000000282846 035 $a(SSID)ssj0000300650 035 $a(PQKBManifestationID)11253260 035 $a(PQKBTitleCode)TC0000300650 035 $a(PQKBWorkID)10252689 035 $a(PQKB)11180995 035 $a(DE-He213)978-3-540-72234-2 035 $a(MiAaPQ)EBC3036615 035 $a(MiAaPQ)EBC6351734 035 $a(PPN)123162025 035 $a(EXLCZ)991000000000282846 100 $a20210218d2007 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIterative approximation of fixed points. /$fVasile Berinde 205 $a2nd ed. 2007. 210 1$aBerlin, Germany ;$aNew York, New York :$cSpringer,$d[2007] 210 4$dİ2007 215 $a1 online resource (XV, 326 p.) 225 1 $aLecture notes in mathematics ;$v1912 300 $a"Originally (1st edition) published by Editura Efemeride, Baia Mare, Romania, 2002"--T.p. verso. 300 $aRevised thesis (doctoral) - Universitatea Babes-Bolyai, Cluj-Napoca. 311 $a3-540-72233-5 320 $aIncludes bibliographical references (pages [221]-304) and indexes. 327 $aPre-Requisites of Fixed Points -- The Picard Iteration -- The Krasnoselskij Iteration -- The Mann Iteration -- The Ishikawa Iteration -- Other Fixed Point Iteration Procedures -- Stability of Fixed Point Iteration Procedures -- Iterative Solution of Nonlinear Operator Equations -- Error Analysis of Fixed Point Iteration Procedures. 330 $aThe aim of this monograph is to give a unified introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. It summarizes the most significant contributions in the area by presenting, for each iterative method considered (Picard iteration, Krasnoselskij iteration, Mann iteration, Ishikawa iteration etc.), some of the most relevant, interesting, representative and actual convergence theorems. Applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods, are also presented. Due to the explosive number of research papers on the topic (in the last 15 years only, more than one thousand articles related to the subject were published), it was felt that such a monograph was imperatively necessary. The volume is useful for authors, editors, and reviewers. It introduces concrete criteria for evaluating and judging the plethora of published papers. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1912. 606 $aFixed point theory 606 $aIterative methods (Mathematics) 606 $aFixed point theory$vBibliography 606 $aIterative methods (Mathematics)$vBibliography 615 0$aFixed point theory. 615 0$aIterative methods (Mathematics) 615 0$aFixed point theory 615 0$aIterative methods (Mathematics) 676 $a518.26 700 $aBerinde$b Vasile$f1955-$0320667 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910485153103321 996 $aIterative approximation of fixed points$9714481 997 $aUNINA