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Agarwal R.P., O'Regan D. — Fixed Point Theory and Applications
Agarwal R.P., O'Regan D. — Fixed Point Theory and Applications



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Название: Fixed Point Theory and Applications

Авторы: Agarwal R.P., O'Regan D.

Аннотация:

Cambridge Tracts in Mathematics vol. 141

For researchers and graduate students in relevant areas of analysis, Agarwal (National U of Singapore), Maria Meehan (Dublin City U.), and Donal O'Regan (National U. of Ireland-Galway) explain the fixed point theory. Beginning with the best known result, Banach's contraction theorem, they develop most of the main results and techniques, establish results for several classes of maps, and present the three main approaches to establishing continuation principles. Exercises are provided for courses or self-study.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 180

Добавлена в каталог: 03.12.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{1}$ homotopy      148
$L^{p}$-Caratheodory function      8
$L^{p}$-Caratheodory solution      8
$L^{p}$-Lipschitz      8
$\delta$-based $\epsilon$-maps      69
$\epsilon$-fixed point      37
$\epsilon$-map      70
$\epsilon$-map in the narrow sense      70
0-epi map      108
Abstract economy      126
Affinely independent      130
Asymptotic centre      116
Asymptotic radius      116
Banach’s contraction mapping principle      1
Banach’s contraction mapping principle for multivalued contractions      112
Banach’s contraction mapping principle, generalisation      5
Banach’s contraction mapping principle, local version      3
Boundary (n-1)-simplex      131
Boundary value problem      101
Brouwer’s fixed point theorem      29 150
Class $C^{1}$      29
Compact      36
Compact field      69
Compactly positive      26
completely continuous      56
Condensing      46
Contraction      1
Crease      143
Critical point      143
Critical value      143
Degree      144
Demiclosed      18
Demicompact      93
Dirichlet problem      22
Discrete boundary value problem      40
Equilibrium point      126
Essential      65 73
Fixed point property      28
Fredholm alternative      72
Fredholm integral equation      49 85
Furi — Pera type theorem      99
Generalised Nash equilibrium point      126
Homeomorphic      28
Homeomorphism      28
Homotopic compact maps      66
Homotopic condensing maps      73
Homotopic continuous maps      150
Homotopic contractions      19
Homotopic multivalued contractive mappings      114
Homotopy of compact transformations      154
Inessential      65 73
Initial value problem      6
k-face      130
k-set contractive      56
KKM covering      133
KKM theorem      132
Krasnoselskii’s compression of a cone theorem      79
Krasnoselskii’s expansion of a cone theorem      82
Kuratowskii measure of noncompactness      46
Ky Fan’s fixed point theorem      136
Ky Fan’s minimax theorem      134
Leray — Schauder degree      153
Lipschitz constant      1
Lipschitzian      1
LL-Caratheodory function      105
Lower semicontinuous      134
Moench’s condition      54
Moench’s fixed point theorem      40
Multiple fixed points      84
Multivalued contractive mapping      112
Multivalued nonexpansive mapping      112
n-simplex      130
Nadler’s fixed point theorem      113
Nonexpansive      1 12
Nonlinear alternative of Leray — Schauder type      18 151
Nonlinear alternative of Leray — Schauder type for $\Phi^{*}$ maps      122
Nonlinear alternative of Leray — Schauder type for closed, multivalued maps      138
Nonlinear alternative of Leray — Schauder type for continuous, compact maps      48 60
Nonlinear alternative of Leray — Schauder type for continuous, condensing maps      56
Nonlinear alternative of Leray — Schauder type for continuous, k-set contractive maps      56
Nonlinear alternative of Leray — Schauder type for contractive maps      21
Nonlinear alternative of Leray — Schauder type for Moench type maps      54
Nonlinear alternative of Leray — Schauder type for multivalued contractive maps      115
Nonlinear alternative of Leray — Schauder type for multivalued nonexpansive maps      117
Nonlinear alternative of Leray — Schauder type for nonexpansive maps      16
Nonlinear alternative of Leray — Schauder type in Frechet spaces      100
Nonlinear alternative of Leray — Schauder type in Hausdorff locally convex linear topological spaces      98
Nonvanishing      30
Normed      30
P-point      143
Paracompaet      120
Picard — Lindeloef theorem      7
Quasibounded      63
Quasiconcave      134
Quasiconvex      134
Quasinorm      63
Regular sequence      116
retract      28
Retraction      28
Sadovskii’s fixed point theorem      40
Schauder projection      36
Schauder — Tychonoff theorem      96
Schauder’s approximation theorem      37
Schauder’s fixed point theorem      38 156
Schauder’s fixed point theorem for nonexpansive maps      12
Simplicial subdivision      131
Sperner's combinatorial lemma      131
Strongly continuous      58
Tangent      30
Triangulation      131
Type $\Phi^{*}$      120
Upper semicontinuous      134 135
Vertices      130
Weakly contractive      26
Weighted maximum norm      7
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