Hyers D.H., Isac G., Rassias T.M. — Stability of functional equations in several variables :: Электронная библиотека попечительского совета мехмата МГУ

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Hyers D.H., Isac G., Rassias T.M. — Stability of functional equations in several variables

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Название: Stability of functional equations in several variables

Авторы: Hyers D.H., Isac G., Rassias T.M.

Аннотация:

The notion of stability of functional equations has been an area of revision and development for the past 20 years, having its origins more than half a century ago when S. Ulam posed the fundamental problem and D. H. Hyers gave the first significant partial solution. This volume is unique in that (to date) none exists as a comprehensive examination to the subject.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 317

Добавлена в каталог: 08.12.2009

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Предметный указатель

$Q_{+}$ -homogenous      205
$R^{N}_{+}$ -admissible      36
$R^{N}_{+}$ -asymptotically equivalent      38
$R^{N}_{+}$ -homotopic      37
$\delta$ -biadditive      51
$\delta$ -multiplicative      112
$\delta$ -multiplicative element      112
$\delta$ -quadratic      45
$\omega^{*}$ -topology      116
$\psi$ mapping      17
$\psi$ -additive mappings      31
$\varepsilon$ -convex      166 170
$\varepsilon$ -midconvexity      175
$\varepsilon$ -quasiconvex functions      176
$\varepsilon$ -subharmonic      179
$\varepsilon$ -Wright-convex      170
2-divisible group      179
A-orthogonal pairs      4
A-orthogonal pairs, additive on      55
A-orthogonal pairs, approximately additive on      56
Abelian groups      105
Abelian groups, compact      131
Abelian groups, infinite      88
Abelian groups, locally compact      123
Abelian groups, torsion-free divisible      262
Absolute minimum      236
Abstract polynomials      155
Accumulation points      114
Additive $\varepsilon$ - mappings      1
Additive function      1
Additive outside a ball      44
Additive selection      210
Algebra      111
allocation      35
Almost approximately convex functions      178
Almost linear      25
Almost linear functional      26
Amenable C*-algebra      131
Amenable left      86 90
Amenable right      86 91
Amenable semigroup      3
AMNM algebras      112
Analytic      123
Antilinear      189
Antilinear isometry      190
Approximate homomorphisms      2
Approximate identity      113
Approximately additive mappings      25 27
Approximately convex functions      6 169 179
Approximately linear mappings      22
Approximately multiplicative functions      3
Approximately multiplicative mappings      102 105
Approximately quadratic      5
Approximately subharmonic functions      179
Asymptotically differentiate      20 31
Automorphism      1
Baire property      279
Baire set      249
Baire space      248
Baire, condition of      250
Baire, measurable      248
Balanced neighborhood      212
Banach algebras      103
Banach algebras, commutative      119
Banach algebras, commutative complex      112
Banach algebras, commutative radical      121
Banach spaces      1 15
Banach spaces, complex      85
Banach spaces, reflexive      234
Banach — Steinhaus theorem      229
Banach — Steinhaus theorem uniform boundedness      286
Best possible approximation      156
Biadditive function      45
Bidisc algebra      123
Bifurcation from infinity      34
Bilinear functional C      112
Binary intersection property      92
Binary relation      78 192
Birkhoff — James orthogonality      192 193
Borel measurable      254
Bounded invertible linear operators      130
Bounded nth-difference      156
Bounded sections      150
Boundedly complete lattice      283
Boundedly complete lattice, Banach      92
Calculus of variations      233
Cancellation corollary      215
Cancellation lemma      215
Cantor's intersection theorem      211
Cauchy convergence criterion      12
Cauchy difference      2 80 263
Cauchy equation      1
Cauchy exponential equation      150
Cauchy sequence      185
Cayley numbers      103
Celestial mechanics      191
Chain      225
Characters      112
Christensen measurable      250
Christensen measure zero      250
Closed ideal      118 123
Closed subspace      182
Commutative domain space      81
Commutative field      139
Commutative semigroup      78
Compact group      130
Compact mapping      30
Compact topological group      130
Complementarity Problem classical Fold      35
Complementarity Problem Fold      35
Complementarity Problem General Order      36
Complementarity Problem Order      35
Complementarity theory      34
Complete metric space      229
Complete orthonormal system      180
Complex conjugate      85 189
Complex Hilbert space      130
Complex normed algebra      3
Complex normed space      123
Complexification      151
Cone      157
Cone, dual      30
Cone, generating      30
Cone, normal      30
Cone, solid      30
Cone, tangent      238
Conjugate space      286
Constraints      237
Consumption set      35
Continuous function      6
Continuous homomorphism      130
Continuously divisble      272
Contractions k-set      30
Contractions strict-set      31
Convex combination x      166
Convex functions      166
Convex hull      83 168
Convex subset      166
Convexity      169
Convolution      113
Convolution algebra      121
Convolution power      121
Cyclic group      111
D'Alembert equation      147—148
Decent      255
Decent rational character      256
Derivative      32
Derivatives at infinity      43
Derivatives at infinity along K      31
Descending countable collection      211

Descending sequence      213
Deterministic case      34
Diagonal map      151
Diagonalization      156
Diameter      212
Difference operator      155
Difference theorem      250
Differentiable almost everywhere      282
Dini      289
Direct method      1 14
Direct sums      182
Directed system      207
Disc      21
Disc algebra      123
Discontinuous additive function      173
Discrete amenable group      131
Discrete group      84
Discrete subgroup      246 267
Distributive problems      35
Divisible group      259
Dixmier's theorem      90
Double integral      122
Dual space      131
Element of infinite order      82
Equivalence, uniform      95
Equivalence, usual      95
Equivalent metrics      98
Equivalent norm      107
Exponential      104
Exponential functions      147
Extension      247
Finite group      85
Finite intersection property      207
Finite interval      156
First variation      237
Fixed end conditions      235
Frechet differential      243
Frechet functional equations      6 155
Free group      81
Functional congruences      9 192 246 255
Functional congruences composite      262
Functional inequality      1
G-character      255
Gajda — Badora — Ger theorem      283
Gateaux differential      237
Gelfand's formula      30
Generalized Dini      288
Generalized orthogonality functional equation      7 180
Generalized polynomial      156
Generators      87
Ger — Tabor theorem      129
Green's theorem      166
Group algebra      131
group characters      255 261
Group of rotations      130
Group representations in quantum mechanics      189
Groupoid      80 93
Haar measure      123 261
Haar measure, positive      261
Hahn — Banach extension property      92 283
Hahn — Banach theorem      87
Hamel basis      178 251
Hammerstein equation      33 310
Hausdorff distance      205
Hausdorff space      80
Hilbert lattice      36
Hilbert space      4
Hoelder's inequality      236
Hoelder's integral inequality      242
Homeomorphic isomorphisms      93
Homeomorphism      272
Homogeneous of degree p      125
Homomorphism      1
Homomorphism, stable equation of      80
Homotopy      36
Hyers — Ulam — Rassias stability      25 282
Hyperbolic functions      154
Hyperplane      116
Idempotent      80 101
Identity elements      98
Immersion      36
inclusion      204
Increments      155
INDEX      1 37
index zero      37
Infinite dimensional vector spaces      178
Infinite sequences      123
Injective      95
Inner automorphism      107
Inner product      261
Inner product space      192
Intermediate value property      233
Invariance      92
Invariance condition      283
Invariance Theorem      99
Invariant      86
Invariant means      84
Invariant measure      84
Invariant vector spaces      154
Isomorphic groupoids      101
Isomorphic groups      99 101
Isoperimetric problem      241
Jensen convex      169
Jensen equation      95
Jordan block      107
Jordan canonical form      107
K-additive functions      155
k-form      156 159
K-set contractions      30
K-valued functions      103
Krein — Rutman theorem      32
Kuratowski — Zorn Lemma      225
Lagrangian function      238
Law of the mean      233
Lebesque measurable      246
Left invariant mean      85 90
Level sets      176
Linear homotopy      39
Linear hull      193
Linear isometry      182 190
Linearly independent modulo      139
Lipschitz property      288
Lipschitzian      287
Lobacevskii's functional equation      134
Local boundedness      169
Local minimum point      233
Locally compact Hausdorff space      123
Locally convex space      83
M-dimensional simplex      168
Manifold      175
Measurability on rays      255
Measurable solution      204
Measure of noncompactness      30
Method of invariant means      2 79
Metric group      1 100
Metric rational vector space      262
Midconvexity      169
Mild regularity conditions      285
Minimal element      225
Minimal quadratic set-valued functions      225
Minimizing curve      237
Minimizing net      234
Minimizing sequence      236
Minimum problem      238
Modulus      191
Monoid      151
Multifunctions      205
Natural logarithm      129
Near multiplicative functionals      112
Necessary condition      239

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