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Yuan G.X.-Z. — KKM Theory and Applications in Nonlinear Analysis
Yuan G.X.-Z. — KKM Theory and Applications in Nonlinear Analysis

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Название: KKM Theory and Applications in Nonlinear Analysis

Автор: Yuan G.X.-Z.

Аннотация:

This reference provides a lucid introduction to the principles and applications of Knaster-Kuratowski-Mazurkiewicz (KKM) theory and explores related topics in nonlinear set-valued analysis.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 621

Добавлена в каталог: 19.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$2^{X}$-notation      22
$A^{C}$-notation      201
$C^{0}$-notation      215 475
$D(A_{1}, A_{2})$-notation      420
$F_{\sigma}$-set      280
$G_{A}$-notation      182
$G_{\delta}$-set      279
$H^{+}_{\phi, \sigma}$-notation      30
$H^{-1}_{\phi, \sigma}$-notation      30
$H^{p}$-space      98
$H_{CO}$-notation      46
$H_{\phi, \lambda}$-notation      24
$I_{X}(x)$-notation      133
$I_{X}(y)$-notation      97
$K\mathcal{A}(X)$-notation      193
$L(X \times Y, Z)$-notation      500
$Max_{W}A$-notation      486
$Min_{W}A$-notation      486
$M_{\phi, \lambda}$-notation      23
$M_{\psi, \lambda}$-notation      30
$N_{x}$-notation      22
$O(x_{0}, \epsilon)$-notation      127
$O_{X}(x)$-notation      133
$O_{X}(y)$-notation      97
$S_{A}(D, S, T)$-notation      343
$S_{A}(X, S, T)$-notation      344
$S_{B}(D, S, T)$-notation      343
$U(B; \omega)$-notation      337
$U(\delta, A)$-notation      344
$U(\delta, x)$-notation      344
$U(\epsilon, A)$-notation      127
$[f=\alpha]$-notation      29
$[f>\alpha]$-notation      29
$[f\geq \alpha]$-notation      29
$[f\leq \alpha]$-notation      29
$\bar{S}$-notation      22
$\delta(X)$-notation      132
$\delta_{E}(X)$-notation      98 100
$\Delta_{N}$-notation      1
$\Delta_{N}^{k}$-notation      46
$\gamma$-DCX ($\gamma$-DCV)-notation      335
$\gamma$-DQCX (DQCV)-notation      335
$\mathcal{A}(M)$-notation      159
$\mathcal{F}$-notation      44
$\mathcal{F}(X)$-notation      22
$\mathcal{G}\ \epsilon-dominates\ \mathcal{F}$-notation      533
$\mathcal{N}(x)$-notation      28
$\mathcal{P}_{0}(X)(=2^{X})$-notation      84
$\mathcal{U}$-notation      153
$\partial \Delta_{N}$-notation      46
$\partial_{E}(X)$-notation      98
$\Pi_{j\neq i, j\in I}Y_{j}\otimes A_{i}$-notation      72
$\preceq$-notation      560
$\Psi(D)$-notation      306
$\succeq$-notation      15 520
$\succeq_{i}$-notation      15
(GQVI(X; F, T))-notation      326
aff(A)-notation      316
Assumption (A)      18
Baire category      20 572
C(X, Y, $\theta$)-notation      243
C(Y)-notation      465
C-space      45
CB(H)-notation      366
Characterization, complementarity      460
Characterization, generalized metric KKM      163
Characterization, set-valued mapping      21
Characterization, topological intersection      206
CK(X)-notation      93
CL(X)-notation      93
clS-notation      22
clT(x)-notation      233
coA-notation      141
Compact, boundary      30
Compact, C-      114
Compact, locally      410
Component      94
Condition, (C')      245
Condition, (C)      244 255
Condition, (C)''      245
Condition, (D)      425
Condition, (E)      423
Condition, (LC)      80
Condition, (P)      220
Condition, (WC)      279
Condition, coercive      461
Condition, non-compact (WC)      279
Condition, strongly Karamardian      456 457
Condition, weakly coercive      461
Cone      429
Cone, corrected      509
Cone, dual      476
Cone, extreme point      476
Cone, normal      560
Cone, pointed      475 486
Cone, positive      560
Cone, solid      475
Differential      356
domS-notation      242
Economy, abstract      7 229 237 252
Economy, most product      572
Economy, production      566
Equilibrium, approximate      256 262 280
Equilibrium, free disposal price      546
Equilibrium, Nash      530
Equilibrium, Pareto      521
Equilibrium, Pareto weak      521
Equilibrium, weight Nash      521 522
Equilibrium, weight normalized Nash      521
Essential complementarity problem      454
Essential component      94 134 354 457
Essential equilibrium      541 571
Essential fixed point      195
Essential KF point      4
Essential set      94
Essential solution      452
Essential variational inequality      353
Essential, weakly      353
F(A)-notation      160
F*-notation      201
F-sequence      554
F-set      45
Family, $KF(X, Y_{i})_{i\in I}$      74
Family, $L(X, X_{i})_{i\in I}$      71
Family, $L_{S}(X, Y_{i})_{i\in I}$      71
Family, $M(X, X_{i})_{i\in I}$      71
Family, $M_{S}(X, Y_{i})_{i\in I}$      71
Family, CK(X)      93
Family, CL(X)      93
Family, exceptional      452 459 461
Family, KF      277
Family, pseudo-base      567
Family, regular      270
Fan, alternative theorem      408
Fan, best approximation      40 112 149 150
Fan, coincidence theorem      3
Fan, geometric lemma      38 140
Fan, inward mapping      100
Fan, matching theorem      113 124
Fan, minimax inequality      4 86
Fan, outward mapping      100
Fan, section theorem      140 141
Fixed point, Brouwer      393
Fixed point, Browder — Fan      59 173 187 244 523 616
Fixed point, Browder — Fan in H-spaces      491
Fixed point, Browder — Fan in hyperconvex spaces      170
Fixed point, Browder — Fan in MC-spaces      185
Fixed point, Fan — Glicksberg      2 121 127 189 273 522
Fixed point, Fan — Glicksberg in locally convex H-spaces      154
Fixed point, Fan — Glicksberg in locally G-convex spaces      191
Fixed point, Fan — Glicksberg in locally MC-spaces      187
Fixed point, Himmelberg      443
Fixed point, Joo      214
Fixed point, Joo and Soevergjarto      207
Fixed point, Schauder — Tychonoff      173
Fixed point, Tarafdar      60
Fixed point, topological      214
Free disposal equilibrium price      17
Function, $\gamma$-diagonally convex (concave)      335
Function, $\gamma$-diagonally quasi-convex (concave)      335
Function, 0-diagonal concave      328
Function, 0-diagonal quasi-concave      328
Function, compactly lower semicontinuous      329
Function, convex      465
Function, monotonically increasing      488
Function, proper      554
Function, qauasi-convex (concave)      335
Function, quasi-convex      465
Function, restriction of      183
Function, strictly H-quasiconvex      489
Function, strictly monotonically increasing      488
Function, strongly monotonically increasing      488
Function, subdifferential      437
Function, subgradient      437
Game, Banach — Mazur      21
Game, constrained N-person      333
Game, cooperative      7
Game, generalized      7 229 237
Game, generalzied      252
Game, multi-criteria      14 463
Game, multi-objective      526
Game, n-person      229
Game, non-cooperative      7
Game, non-cooperative n-person      530
Game, one-person      236 250
Game, qualitative      236 251
Game, theory      6 7
Game, zero-sum      15 487
GCP'-notation      445
GCP-notation      445
Generalized sequence      557
Generic stability      19
Generic study method      18
GQVI(A)-notation      344
GQVI(B)-notation      344
GQVI(X; A; B)-notation      10
GSQVI-notation      367
GVVLI-notation      358
h(A, B)-notation      135
H-space      45
Inequality, Fan's minimax      2
Inequality, generalized quasi-variational      10 390
Inequality, generalized variational      390
Inequality, Ha minimax      145
Inequality, Kneser minimax      422
Inequality, Lions — Stampacchia variational      409
Inequality, Sion minimax      70
Inequality, topological minimax      221
Inequality, vector minimax      508
intS-notation      22
K(X)-notation      84 127
k-face-notation      42
k-set      247
k-space      247
KF-point      89
Kindler's question      209
KKM, covering      1
KKM, dual form      41 44
KKM, generalized KKM mapping      4
KKM, mapping      4
KKM, principle      3 38
KKM, theorem      1 38
KKM, theory      1 3 84
Lemma, Debreu — Gale — Nikaido      17 409 545 546
Lemma, Deguire and Lassonde      63 74
Lemma, DGN      546
Lemma, Ding and Tan      150
Lemma, Fan      243
Lemma, Fan's geometric      1
Lemma, Fort      127
Lemma, generalization of DGN      551
Lemma, Horvath      161
Lemma, Kindler      202
Lemma, Luc      357
Lemma, Park et al.      141
Lemma, Riesz      27
Lemma, Sperner's      42
Lemma, Tan and Yuan      396
Lemma, Tarafdar      154
Lemma, Zhou and Tian      48
Lipschitz      356
M'-notation      93
MAP      62
Mapping of class $KF_{\theta}(KF_{\theta, C})$      233
Mapping of class $L_{\theta, C}$      274
Mapping of class $\mathcal{L}_{\theta}$      289
Mapping of class $\mathcal{U}_{\theta}$      300
Mapping upper approximating      270
Mapping upper demicontinuous (UDC)      23
Mapping upper hemicontinuous      116
Mapping upper hemicontinuous(UHC)      23
Mapping upper semicontinuous      84
Mapping upper semicontinuous(USC)      22
Mapping, $F_{\theta}$-majorant      243
Mapping, $F_{\theta}$-majorized      243
Mapping, $KF_{\theta} (KF_{\theta, C})$      233
Mapping, $KF_{\theta}$- $(KF_{\theta, C})$-majorized      233
Mapping, $KF_{\theta}$-$(KF_{\theta, C})$-majorant      233
Mapping, $L_{S}$-majorant      71
Mapping, $L_{S}$-majorized      71
Mapping, $L_{\theta, C}$-majorant      274
Mapping, $L_{\theta, C}$-majorized      274
Mapping, $\alpha$-$\hat{H}$-Lipschitz continuous      372
Mapping, $\alpha$-strongly monotone      375
Mapping, $\beta$-Lipschitz continuous      375
Mapping, $\beta$-strongly monotone      372
Mapping, $\epsilon$-domination      533
Mapping, $\eta$-pseudo-monotone      359
Mapping, $\lambda$-Lipschitz continuous      372
Mapping, $\mathcal{L}$-majorized      230
Mapping, $\mathcal{L}_{\theta}$-majorant      289
Mapping, $\mathcal{L}_{\theta}$-majorized      289
Mapping, $\mathcal{U}$-majorized      232
Mapping, $\mathcal{U}_{\theta}$-majorant      300
Mapping, $\mathcal{U}_{\theta}$-majorized      300
Mapping, $\mu$-strongly monotone      372
Mapping, $\phi$-monotone      561
Mapping, $\Psi$-condensing      306 307
Mapping, acyclic      306
Mapping, adherence      233
Mapping, almost lower semicontinuous      84
Mapping, C-concavity(convexity)      476
Mapping, C-convex      490
Mapping, C-convexlike      490
Mapping, C-quasi-convexity (concavity)      476
Mapping, closed      359
Mapping, compact      233
Mapping, compact-valued      489
Mapping, compactly open      242
Mapping, completely compact      443
Mapping, condensing      307
Mapping, constraint      229
Mapping, continuous      85
Mapping, contraction      131
Mapping, convex (concave)      489
Mapping, convex-values      62
Mapping, couple majorized      40
Mapping, couple-majorant      63
Mapping, couple-majorized      63
Mapping, demicontinuous      489
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