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Aubin J., Frankowska H. — Set-Valued Analysis
Aubin J., Frankowska H. — Set-Valued Analysis

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Название: Set-Valued Analysis

Авторы: Aubin J., Frankowska H.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 461

Добавлена в каталог: 09.01.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\delta$-generalized gradient      249
$\sigma$-algebra      306
$\sigma$-finite measure      306
Adjacent cone      126
Adjacent derivative      189
Adjacent epiderivative      237
Approximate selection      358
Asymptotic cone      159
Asymptotic epiderivative      300
atom      329
Attouch's theorem      299
Baire's theorem      44 58
Ball      17
Biorthogonal subspace      63
Bipolar cone      63
Bipolar set      63
Bipolar theorem      64
Bipolar theorem for closed convex processes      70
Bitranspose      67
Borel $\sigma$-algebra      306
Bounded family of processes      61
Bounded-valued map      36
Caratheodory map      311
Caratheodory parametrization      376
Caratheodory selection theorem      374
Castaing's theorem      319
Cellina's theorem      358
Characterization of monotone maps      107
Choquet's theorem      163
Circatangent cone      127
Circatangent cone to a sequence of sets      166
Circatangent derivative      189
Circatangent epiderivative      237
Clarke normal cone      157
Clarke tangent cone      127
Closed convex process      56 314
Closed convex set-valued map      34 373
Closed graph criterion      73
Closed graph theorem      60
Closed range theorem      64
Closed set-valued map      34 41
Closed-valued map      36 56
Coerciveness      88
Compact-valued map      36
Complementary convex      164
Complete $\sigma$-algebra      307
Complete $\sigma$-finite measure space      310
Complete measure space      307
Composition product      37
Concave function      222
Cone with compact sole      114
Conjugate function      256
Consistent      203
Consistent sequence of functions      96
Constrained inverse function theorem      96 207
Constraint qualification condition      140
Contingent cone      32 121
Contingent derivative      181
Contingent epiderivative      225
Contingent Hessian      299
Contingent hypoderivative      226
Contingently epidifferentiable      225
Continuous partition of unity      81 386
Continuous selection      355
Continuous set-valued map      40 141
Convergence of gradients      295
Convergence of subdifferentials      297
Convergence theorem      271
Convex epiderivative      241
Convex function      222
Convex hull of an upper limit      26 273
Convex kernel      159
Convex set-valued map      34 56
Convex-valued map      36
Core      36
Correspondence      33
COW      119
Criterion of pseudo-Lipschitzeanity      101
Crossed convergence      61
Curvaceous shape      354
Cut set-valued map      43
Dense family of selections      310
Derivable cone      127
Derivable set      127
Derivable set-valued map      182
Differential geometer      119
Differential quotient      94
Dini directional derivative      94
Directed set      19
Distance to a set      17
Domain      34
Dual norm      20
Duality map      125
Duality pairing      19
Duality relation      258
Dubovitskij — Miljutin cone      125
Eigenvalue of a convex process      114
Eigenvector of a convex process      114
Ekeland's rule      91 233
Epicontinuous      285
Epiderivative      225
Epigraph      222
Epilimit      275
Episleek function      225
Equilibrium map      207
Equilibrium theorem      84 276
Extension of a set-valued map      36 236
Extremal element      329
Extremal face      88 343
Extremal selection      330
Fenchel's inequality      256
Fermat's rule      232
Fixed point theorem for inward or outward maps      87 250
Frechet differentiable single-valued map      94 250
Gateaux differentiable single-valued map      94
Generalized gradient (Clarke)      249
Generalized sequence      19
Generic continuity      44
Generic property      44
God (spherical)      119
Gradient      94
Graph of a map      34
Graph of the transpose of a process      67
Graphical convergence      267
Graphical convergence of monotone maps      270
Graphical upper /lower limit of set-valued maps      267
Graves' theorem      95
Hausdorff distance      365
Higher order adjacent subset      171
Higher order circatangent subset      171
Higher order contingent subset      171
Higher order derivatives      216
Higher order epiderivatives      260
Hypertangent cone      164
Hypograph      222
Hypolimit      276
Image of a set-valued map      34
Indicator of a set      223
Inf-compact      281
Injective (globally)      209
Integrably bounded      326
Integral of a set-valued map      327
Intermediate cone      126
Invariant space      72
Inverse image      36
Inverse map      34
Inverse set-valued map theorem      204
Inverse stability theorem      100
Inward map      87
Kakutani's fixed point theorem      87
Kernel of the derivative      187
Kruemmungsschwerpunkte      365
Ky Fan's inequality      80
Labor value      78
Lax's principle      96 99
Leray — Schauder's theorem      90
lim sup inf      192
Limit of infima      281
Limit of set-valued maps      41
Limit of sets      17
Linear extension of a set-valued map      346
Linear process      56
Lipschitz parametrization      379
Lipschitz selection      372
Lipschitz set-valued map      41
Local subdifferential      253
Local superdifferential      253
Local uniqueness criterion      103
Locally injective set-valued map      209
Lop-sided paratingent derivative      201
Lower Dini derivative      231
Lower epicontinuous      285
Lower epilimit      276
Lower hypolimit      276
Lower limit of set-valued maps      41
Lower limit of sets      17
Lower semicompact      281
Lower semicontinuity criterion      49
Lower semicontinuous set-valued map      39
Lower semicontinuously differentiable map      188
Lyapunov's Convexity theorem      339
Lyapunov's Convexity theorem (in Banach spaces)      340
Marginal function      48
Mathematical striptease      93
Maximal monotone map      106
Maximum theorem      48 258
Mazur's theorem      271
Measurable      307
Measurable (single-valued map)      307
Measurable selection      308
Measurable space      306
Measurable/Lipschitz map      373
Measurable/Lipschitz selection theorem      375
Michael's theorem      355
Minimal map      360
Minimal selection theorem      363
Minimum (bare)      93
Minkowski's difference of sets      159
Minty's theorem      108
Minty's trick      108
Monotone map      104
Moreau — Yosida's approximation      258
Moreau's theorem      258
Mosco's theorem      290
Multifunction      33 258
Multivalued function      33 270
Negative polar cone      63
Nonatomic measure      329
Nontrivial extended function      222
Nontrivial set-valued map      34
Norm of a process      57
Normal cone to a convex subset      139
Normal cone to a set      157
Open mapping theorem      57
Oresme — Fermat's rule      219
Orthogonal      63
Outward map      87
Paratingent cone      162
Paratingent cone to a sequence of sets      167
Paratingent derivative      201
Paratingent epiderivative      241
Poincare's continuation method      89 201
Point to set map      33
Pointwise convergence of set-valued maps      268
Pointwise inverse function theorem      101
Pointwise limit of set-valued maps      313
Polar cone      25 63
Polar of a viability domain      144
Polar set      28 63
Polish space      306
Positive polar cone      63 146
Positively homogeneous function      222
Positively homogeneous set-valued map      56
Process      56
Product of set-valued maps      37
Projection      125
Proper map      28
Proper set-valued map      43
Pseudo-convex function      233
Pseudo-convex set      145
Pseudo-convex set-valued map      182
Pseudo-Lipschitz set-valued map      41
Reflexive space      20
Residual      44 163
Resolvent of a monotone map      106
Restriction of a single-valued map      34 182
Robinson — Ursescu's open mapping theorem      58 194
Rocquefort      321
Sauterne      321
Selection of a set-valued map      355
Separable space      20
Separation theorem      64
Sequentially inf-compact      281
Sequentially weak upper limit      20
Set-valued Graves' theorem      205
Set-valued map      33
Shi Shuzhong's theorem      165
Simple map      307
simplex      82
Sleek set      101
Sleek set-valued map      182
Smooth Banach space      125
Sole of a cone      114
Solvability theorem      85 130
Square product of set-valued maps      37
Stability assumption      96
Stable family of set-valued maps      203
Star-shaped set      145
Steiner point      365
Strict set-valued map      34
Strictly convex space      360
Striptease (mathematical)      93
Strong convergence of a sequence in a Lebesgue space      272
Strong measurability      307
Subdifferential      248
Subgradient      248
Support function of a set      62
Support function of the transpose      75
Surjective closed convex process      57
Tangent cone to a convex cone      143
Tangent cone to a convex set      83 138
Tangent cone to a finite intersection      149
Tangent cone to a sleek subset      130
Tangent cone to direct image      153
Tangent cone to inverse image      148
Tangent cone to the interior of a set      140
Tangentially regular      127
Tarte Tatin      321
Transpose of a process      67
Transpose of a product      68
Transpose of the restriction      69
Transversality condition      32 96 147
Uniform boundedness theorem      61 152
Uniformly sleek set      101
Uniformly sleek set-valued map      205
Uniformly smooth      133
Unit ball      17 158
Upper epicontinuous      285
Upper epilimit      275
Upper hemicontinuous map      74 175
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