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Berinde V. — Iterative Approximation of Fixed Points
Berinde V. — Iterative Approximation of Fixed Points

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Название: Iterative Approximation of Fixed Points

Автор: Berinde V.

Аннотация:

The aim of this monograph is to give a unified introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. It summarizes the most significant contributions in the area by presenting, for each iterative method considered (Picard iteration, Krasnoselskij iteration, Mann iteration, Ishikawa iteration etc.), some of the most relevant, interesting, representative and actual convergence theorems. Applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods, are also presented. Due to the explosive number of research papers on the topic (in the last 15 years only more than one thousand articles related to the subject were published), it was felt that such a monograph was imperatively necessary. The volume is useful for authors, editors, and reviewers. It introduces concrete criteria for evaluating and judging the plethora of published papers.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second

Год издания: 2007

Количество страниц: 332

Добавлена в каталог: 03.12.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\varphi$-contraction      42 167
$\varphi$-contraction, generalized      129
$\varphi$-contraction, strict      166 173 174
${n}^{th}$ iterate of T      3
${n}^{th}$ iterate of x under T      3
(c)-$\varphi$-contraction      167
(c)-comparison function      41 167
(c)-comparison function, subadditive      167
a-contraction      6 77 172 200
a-contraction, multivalued      170
Aamri      221
Abbaoui      221
Abel means      144
Achari      221 267 276
Agarwal      175 221 222 254 286 303
Agratini      222
Ahmad      222
Ahmed      154 222
Akhiezer      222
Aksoy      222
Akuchu      273 274
Alber      83 154 222 223
Algetmy      223
Ali      234
Allgower      223
Almost weak stability      165
Alspach      87 223
Altas      223
Amer      223
AN      248 264
Aneke      235 237
Angelov      223
Aniagbosor      273
Approximate fixed point sequence      145 155
Approximate operator      166 167
Approximate sequence      158 162—165
Argyros      223
Asad      222
Aslam Noor      223 256 296 298
Asplund      223
Assad      223
Asymptotic center      144 145
Athanasov      223
Atsushiba      224
Averaged map      65
Averaged mapping      81
Averaged operator      73 79
Azam      226
Babadzhanyan      224
Babu      110 134 219 224 267 284
Badshah      284
Baek      225
Bai, B.R.      250
Bai, C      225
Bai, M.      225
Baillon      87 152 225 292
Banach      8 27 57 225
Banach orbital condition      53 55 59
Banach space      7 91 102 104 107 128 129 132 142 161 180 184 212
Banach space, finite dimensional      174
Banach space, infinite dimensional      174
Banach space, q-uniformly smooth      11 188 189 198
Banach space, real      146 147
Banach space, reflexive      9 174 193
Banach space, separable      122 174
Banach space, smooth      11 198
Banach space, strictly convex      80 81 93 94
Banach space, uniformly convex      8 67 79 95—97 100 125 128 138 144 210
Banach space, uniformly smooth      11 109 117 121 136 144 149 186 192
Banach space, with Frechet differentiable norm      122 124
Banach space, with uniformly Gateaux differentiable norm      147
Banach's fixed point theorem      37
Bandyopadhyay      244
Bao, K.Z.      225
Bao, Z.Q.      225
Barbu      196 226
Barnsley      226
Bauschke      154 226
Beauzamy      226
beg      226
Berinde, M.      219 226 228
Berinde, V.      27 43 57 58 84 110 175 176 196 218 219 226—228
Bessaga      58 228
Bessaga mapping      39
Bethke      110 228 260
Bezanilla Lopez      228
Bidual space      9
Bielecki      229
Bielecki metric      5 24
Binh      85 229
Bisection method      216
Bogin      110 229
Bohl      229
Bolen      229
Borwein, D.      229
Borwein, J.M.      229
Bose, R.K.      229
Bose, S.C.      229
Bounded set      8 18 61 63—65 67—70 83 85—88 95 97 98 104 109 117 118 120—122 125 134 140 142 143 145—147 149 152 153 155 160
Bounias      264 285
Boyd      27 60 229
Boyd — Wong fixed point theorem      45
Branciari      229
Brezinski      229
Brezis      229
Brimberg      229
Brosowski      229
Browder      27 61 83—85 88 96 110 153 154 180 181 229 230
Browder — Gohde — Kirk fixed point theorem      63 97
Browder's fixed point theorem      45
Bruck      87 133 152 153 156 225 230
Bruckner      230
Bryant      59 230
Butnariu      230 231
Bynum      231
Caccioppoli      231
Carbone      231
Cass      231
Catinas      231
Cauchy sequence      5 32
Cauchy — Schwarz inequality      66 72
Censor      231
Cesaro matrix      91
Cesaro mean      18 143 152
Chaira      221
Chang      133 175 196 225 231 232 275 303 304
Charnay      282
Chatterjea      58 232
Chatterjea operator      131
Chatterjea's fixed point theorem      37
Chebyshev metric      5 23
Chebyshev norm      86
Chen, D.Q.      244 245 303 304
Chen, F.Q.      232
Chen, J.L.      232
Chen, K.      298
Chen, M.P.      232 233
Chen, N.      233
Chen, R.D.      233 248 289 298
Chen, Y.Z.      233
Chen, Yan      233
Chen, Ying      295
Cheng      233
Chiaselotti      233
Chidume, C.E.      27 110—112 133 151 152 154 155 175 192 196 198 222 233—237
Chidume, CO.      235
Chitescu      223
Cho      175 196 221 222 225 231 232 237 250 251 254 255 261 265 266 275 276 284 303 304
Choudhury      237
Chu      238
Chugh      278
Chun      151 152 175 252 257 265
Cioranescu      238
Ciric      39 49 58 62 129 133 134 238
Ciric's contractive condition      54
Ciric's fixed point theorem      49
Closed set      8 15 18 61—65 67—70 73 78 80 81 83—88 90 91 93—97 117 120—122 125 128 129 131 132 134 136 138 140 142—149 152 153 155 160 202 207 210 212—214
Closure      29
Cluster point weak      97
Collacao      238
Combettes      238
Common fixed point      138
Compact set      29 81
comparison function      7 41 77 78 173
Comparison function, 5-dimensional      7 45
Comparison function, strict      41 166 169
Comparison series      44 78 167
Condition (D)      98
Condition A      127
Constantin      238
Continuous dependence of the fixed point      168
Contraction      6 142
Contraction coefficient      33 172
Contraction mapping principle      6 31
Contraction, strict      6 23
Contraction, strictly pseudo $\varphi-$      78
Convergence order      195
Convergence rate, linear      202
Convergence theorem      186
Converse of Banach's fixed point theorem      60
Convex combination      84 142
Convex hull      94
Convex neighborhood      193
Convex set      8 16—18 62—65 67—70 73 78 80 81 83—91 93—98 100 102 104 107 109 112 114 115 117 120—122 125 128 129 131 132 134 136—140 143—149 152 153 155 160 188 202 207 210 212—214
Coppel      239
Crandal      239
Cristescu      239
Crombez      239
Cui, Y.L.      262
d'Apuzzo      223
Dai, A.      239
Dai, H.      239
DAS      151 239
Dashputre      283
Data dependence of fixed points      169 200
Data dependence of fixed points, for multivalued mappings      171
De Amo      223
De Blasi      239
De Pascale      233 240
Debata      151 239
Debnath      245 293
Deimling      114 239
Deng      126 133 239 240 242 253 262 292 296
Deshpande      27 285
Deutsch      240
Dhage      240
Di Lena      241
Diaz Carillo      223
Diaz, J.      57 83 238 240
Diestel      240
Ding      133 240—242
Dirichlet summability      144
disconnected set      86
Distance      4
Distance, induced by the norm      7
Djafari Rouhani      242
Dominguez Benavides      242
Donchev      242
Dotson      57 61 83 109 110 127 242 244 285
Downing      242
du      247
Dual space      9 187
Duality mapping      120
Duality mapping, generalized      198
Duality mapping, normalized      9 134 187
Duality mapping, single-valued      120
Duality mapping, uniformly continuous      120
Duality mapping, weakly sequentially continuous      144
Duality pairing      9 122
Dubey      294
Dugundji      27 28 58 242 246
Dunn      242 243
Dzitac      243
Eaves      243
Edelstein      57 83 94 152 243
Emmanuele      243
Empirical study      216 219
Enflo      226
Engl      243
Equilibrium point      114
Equivalent metric spaces      29
Equivalent metrics      5
Error estimate      161 200
Error estimate, a posteriori      31 73 168 200
Error estimate, a priori      31 73 168 200 201
Euclidean inner product      72
Euclidean metric      4 29
Euclidean norm      72 98
Evans      243
Evhuta      244
Expanding map      59
Explicit scheme      192
Falkowski      244
Family of operators      168
Fang      175 237 244
Farkhi, E.      242
Fastest iteration      74 213
Fastest Krasnoselskij iteration      75 207
Feathers      244
Feng, C      264
Feng, X.Z.      244
Figueiredo iteration      18 145 160
Fisher      237
Fixed point      3 63 69 70 73 78 82 91 94 97 100 102 104 107 114 117 121 125 128 129 142—146 161 163 166 169 201 203 204 210 212
Fixed point iteration method numerically stable      158
Fixed point iteration procedure      157 166
Fixed point iteration procedure, almost T-stable      161 163
Fixed point iteration procedure, stable with respect to T      158 159 163
Fixed point iteration procedure, summable almost stable      176
Fixed point iteration procedure, T-stable      158 160 163
Fixed point iteration procedure, weakly T-stable      163
Fixed point problem      179 185 186
Fixed point property      87 147 188 192
Fixed point, attractive      205 218
Fixed point, of a multivalued operator      170
Fixed point, repulsive      205 218
Fixed points set      104 107 170
Forster      244
Franklin      244
Franks      219 244
Frechet derivative      122
Fredholm integral equation      22
Frum — Ketkov      81 85 88 244
Frum — Ketkov contractive condition      81 88
Frum — Ketkov fixed point theorem      82 88
Fuchssteiner      244
Function, convex      69
Function, decreasing      206 216
Function, lower semicontinuous      69
Function, nondecreasing      204 205
Function, positively homogeneous      19
Function, upper semicontinuous from the right      60
Functional      169
Gairola      287
Gal      244
Ganguly, A.      244
Ganguly, D.K.      244
Gao, C.J      250
Gao, G.L      244 245 304
Gao, W      247
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