國立虎尾科技大學 |

Fixed Point Theorems and Applications

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Fixed Point Theorems and Applications/ by Vittorino Pata.
作者:	Pata, Vittorino.
面頁冊數:	XVII, 171 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Functional analysis. -
電子資源:	https://doi.org/10.1007/978-3-030-19670-7
ISBN:	9783030196707

Fixed Point Theorems and Applications
Pata, Vittorino.

Fixed Point Theorems and Applications[electronic resource] /by Vittorino Pata. - 1st ed. 2019. - XVII, 171 p. 1 illus.online resource. - La Matematica per il 3+2,1162038-5722 ;. - La Matematica per il 3+2,84.

1 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 ε-type 29 -- 6 Sequences of maps and ﬁxed points 36 -- 7 Fixed points of non-expansive maps 39 -- 8 The Riesz mean ergodic theorem 42 -- 9 The Brouwer ﬁxed point theorem 46 -- 10 The Schauder-Tychonoﬀ ﬁxed point theorem 50 -- 11 Further consequences of the Schauder-Tychonoﬀ 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 diﬀerential 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 Hausdorﬀ spaces 118 -- 23 Invariant means on semigroups 120 -- 24 Haar measures 123 -- 25 Game theory 130 -- 26 Problems.

This 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.

ISBN: 9783030196707

Standard No.: 10.1007/978-3-030-19670-7doiSubjects--Topical Terms:

527706
Functional analysis.

LC Class. No.: QA319-329.9

Dewey Class. No.: 515.7

Fixed Point Theorems and Applications
LDR:03405nam a22003975i 4500 001 1012371
003 DE-He213
005 20200703150140.0
007 cr nn 008mamaa
008 210106s2019 gw | s |||| 0|eng d
020 $a 9783030196707 $9 978-3-030-19670-7
024 7 $a 10.1007/978-3-030-19670-7 $2 doi
035 $a 978-3-030-19670-7
050 4 $a QA319-329.9
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.7 $2 23
100 1 $a Pata, Vittorino. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1306624
245 1 0 $a Fixed Point Theorems and Applications $h [electronic resource] / $c by Vittorino Pata.
250 $a 1st ed. 2019.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a XVII, 171 p. 1 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a La Matematica per il 3+2, $x 2038-5722 ; $v 116
505 0 $a 1 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 ε-type 29 -- 6 Sequences of maps and ﬁxed points 36 -- 7 Fixed points of non-expansive maps 39 -- 8 The Riesz mean ergodic theorem 42 -- 9 The Brouwer ﬁxed point theorem 46 -- 10 The Schauder-Tychonoﬀ ﬁxed point theorem 50 -- 11 Further consequences of the Schauder-Tychonoﬀ 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 diﬀerential 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 Hausdorﬀ spaces 118 -- 23 Invariant means on semigroups 120 -- 24 Haar measures 123 -- 25 Game theory 130 -- 26 Problems.
520 $a This 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.
650 0 $a Functional analysis. $3 527706
650 0 $a Partial differential equations. $3 1102982
650 0 $a Differential equations. $3 527664
650 0 $a Topology. $3 633483
650 1 4 $a Functional Analysis. $3 672166
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Ordinary Differential Equations. $3 670854
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030196691
776 0 8 $i Printed edition: $z 9783030196714
830 0 $a La Matematica per il 3+2, $x 2038-5722 ; $v 84 $3 1253905
856 4 0 $u https://doi.org/10.1007/978-3-030-19670-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)