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Berinde V. — Iterative Approximation of Fixed Points
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Название: Iterative Approximation of Fixed PointsАвтор: 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: Рубрика: Computer science /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: secondГод издания: 2007Количество страниц: 332Добавлена в каталог: 03.12.2008Операции: Положить на полку |
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Предметный указатель
Mapping, m-accretive 188 Mapping, monotone 188 Mapping, nonexpansive 6 67 125 138 145 149 160 188 192 Mapping, pseudocontractive 10 114 146 147 156 Mapping, quasi nonexpansive 79 80 Mapping, quasi-contractive 99 Mapping, single-valued 198 Mapping, strict asymptotically pseudocontractive 139 Mapping, strictly pseudocontractive 13 99 Mapping, strictly quasi nonexpansive 81 Mapping, strongly accretive 11 104 Mapping, strongly pseudocontractive 13 104 132 Mapping, sunny 148 Mapping, uniformly accretive 197 Mapping, uniformly asymptotically regular 155 Mapping, uniformly continuous 147 198 Mapping, uniformly L-Lipschitzian 139 Mapping, uniformly pseudocontractive 197 Mapping, uniformly quasi-accretive 198 Mapping, weakly closed 97 Mapping, weakly continuous 97 Mapping, with bounded range 198 Marino 154 233 240 267 Markin 267 Martinez Yanez 259 Maruster 267 Massa 267 268 287 Matrix, strongly regular 145 Matsushita 268 Mazur's theorem 94 Meir 60 268 Meir — Keeler fixed point theorem 60 Melentsov 268 Messano 241 Meszaros 268 Metcalf 57 83 240 Metric 4 Metric projection 148 Metric space 4 157—159 163 166 168—170 Metric space, compact 34 35 Metric space, complete 5 166 167 169—172 Metric space, convex 129 Metric space, locally compact 174 Metrics, metrically equivalent 5 Meyer 268 Michelot 261 Miczko 268 Mikhlin 28 268 Minty 268 Mishra 129 268 287 Misiurewicz 268 Miyaura 268 Miyazaki 268 Modulus of convexity 123 Modulus of smoothness 11 Moloney 268 Moore 27 110 151 198 235 269 Morales 152—154 254 259 269 270 Moreau 270 Mostafa Ali 260 Moudafi 154 270 Mrazec 219 244 Mukherjee 229 270 Muller 270 Multivalued contraction 172 Multivalued mapping, accretive 187 Multivalued mapping, m-accretive 187 189 Multivalued mapping, pseudocontractive 187 Multivalued mapping, strongly accretive 187 Multivalued mapping, strongly pseudocontractive 188 Multivalued mapping, uniformly continuous 198 Multivalued mapping, uniformly quasi-accretive 198 Multivalued operator 170 Multivalued operator, closed 171 Muresan, A.S. 270 Muresan, S. 283 Muresan, V. 270 Musy 282 Mutangadura 111 133 235 270 Myjak 239 Nadler 174 175 270 Naidu 270 Naimpally 117 270 271 Nakajo 154 271 NAM 175 257 266 Nearest point projection 148 Nemytzki 57 271 Neumaier 271 Nevanlinna 196 271 Newton type method high-order 21 Newton — Raphson method 22 216 Newton's method 20 202 Neyman 259 Nguyen 249 Ni, R.X. 244 271 298 Ni, Y.Q. 289 Nnoli 198 235 269 Nonlinear equation 179 199 Nonlinear equation, single 20 Nonlinear ergodic theorem 144 Norm 7 Norm, induced by the inner product 12 Norm, uniformly Gateaux differentiable 188 192 Normed linear space 139 159 187 198 Normed space 7 Normed space, strictly convex 9 Notik 154 222 Ntatin 237 269 Numerical approximation 157 Nussbaum 85 271 O'Brian 243 O'Hara 154 272 O'Regan 272 Oblomskaja 83 272 Ofoedu 235 272 Ogura 298 Olatinwo 251 Operator, 196 Operator, 196 Operator, 186 Operator, 121 134 161 184 Operator, accretive 11 179 Operator, asymptotically pseudocontractive 155 Operator, asymptotically regular 42 80 85 96 Operator, asymptotically regular under T 42 Operator, closed 96 Operator, conditionally quasi-nonexpansive 81 82 Operator, continuous 94 184 Operator, contractive 34 Operator, demiclosed 97 Operator, demicompact 65 70 Operator, generalized pseudocontractive 73 77 207 Operator, hemicontractive 137 Operator, Lipschitzian 72 73 104 107 121 136 139 161 180 207 Operator, locally Lipschitzian 179 193 Operator, m-accretive 193 Operator, nonexpansive 8 37 63 69 77 96 97 138 143 Operator, positively homogeneous 143 Operator, pseudo 77 Operator, pseudocontractive 11 77 179 Operator, quasi nonexpansive 37 62 93 94 96 Operator, quasi-contractive 127 Operator, strictly pseudo 77 78 Operator, strictly pseudocontractive 70 77 136 Operator, strictly quasi nonexpansive 39 Operator, strongly accretive 11 179 180 Operator, strongly monotone 71 72 Operator, strongly pseudocontractive 11 79 104 107 109 117 121 179 Operator, uniformly continuous 186 Operator, weakly closed 97 Operator, weakly continuous 97 Operator, with bounded range 184—186 197 Operator, with unbounded range 185 Opial 83 88 97 122 133 272 Opial's condition 88 122 125 138 Opojzev 272 Ordinary differential equation 19 ORI 296 Ortega 201 202 272 Oscillatory sequence 8 Osilike 27 59 84 110 112 151 154 175 178 196 235 236 272—274 Ostrowski 274 Outlaw 83 274 Owojori 274 p-integrable function 10 Pachpatte 274 Pacurar 228 PAI 294 PAL 267 Palczewski 268 Pan 274 Pandhare 275 Panja 275 Papp 275 Park, E.H. 254 Park, J.A. 275 Park, J.S. 254 Park, J.Y. 110 232 275 Park, K.S. 275 Park, S 275 276 Partial sums 167 Pascali 276 Passty 276 Pathak 276 Patil 276 Patterson 83 276 Pavaloiu 276 Pawar 276 Pazy 239 276 Peitgen 276 Pelczar 276 Peluso 241 Pennanen 238 Petrusel, A. 57 175 276 277 283 Petrusel, G. 57 283 Petryshyn 27 58 61 62 83—85 88 96 110 154 230 277 Pettis — Milman theorem 95 Picard 27 57 277 Picard iteration 3 15 53 75 90 158 164 168 180 200 202 203 206 207 210 212 216 Picard iteration, associated to T 40 167 200 Picard mapping 34 40 44 57 Picard operator 34 36 37 57 59 60 62 166 Picard operator, 171 Picard operator, c-weakly 170 Picard operator, c-weakly multivalued 171 Picard operator, strict 34 Picard operator, weakly 52 58 Pietramala 240 267 Pillay 154 272 Plubtieng 277 Pointwise convergence 173 174 Polar coordinates 98 Potra 277 Prasad 270 Precompact set 127 Precup 277 Precupanu 226 Prehilbertian space 12 Prempeh 154 237 299 Pseudocontraction 12 Ptak 277 Qin 247 Quasi-contraction 22 128 Radovanovic 277 Radu 277 Rajput 278 Rakotch 60 278 Rani 278 Rao 134 Rashwan 278 Rasias 223 Rate of convergence 31 53 74 199 201 202 Rate of convergence, absolute 201 Rate of convergence, asymptotic 202 Rate of convergence, linear 33 Rate of convergence, relative 201 Ray 278 Reflexive Banach space with a uniformly Gateaux differentiable norm 188 Regular matrix 91 Reich 27 84 87 126 133 153 154 197 222 223 225 229—231 242 245 271 279 280 Reich's theorem 189 Reinermann 155 270 280 Ren, W.Y. 280 Ren, X. 280 Retraction 148 Retraction, sunny 144 Retraction, sunny nonexpansive 149 Rheinboldt 201 202 272 Rhoades 27 59 84 109 110 112 127 129 132—134 152 175 177 178 196 199 202 215 219 220 231 248 249 255 280—282 Rihm 280 Roach 110 252 297 Robert 282 Robinson 282 Rode 152 282 Rogers 60 248 Rothe's boundary condition 84 Rouhani 282 Rounding error 157 Roux 241 282 287 Rump 256 RUS 27 44 49 57—59 175 200 222 277 282 283 Saddek 278 Sadok 252 Saha 267 Sahani 229 Sahu 237 254 283—285 294 Saigal 243 Sakaniwa 298 Saliga 259 281 Samanta 275 284 Sastry 110 134 284 Sayyed 284 Sburlan 276 Scarf 284 Schaefer 28 67 83 94 284 Schauder basis 88 Schauder's fixed point theorem 94 115 137 Schilling 284 Schoneberg 225 259 280 284 Schroder 284 Schu 110 152 154—156 284 285 Secelean 223 Sehgal 223 Selfmap 3 Selfmapping 59 Senter 109 110 127 285 Sequence of contractions 174 Sequence of operators 172 Sequence of successive approximations of a multivalued operator 170 Sequence, bounded away 97 Sequence, convergent 5 Sequence, of successive approximations 3 Sequence, uniformly convergent 172 Sequences acceptably paired 156 188 189 192 196 197 Serb 276 Series of positive terms 43 Sessa 84 251 256 281 Shafrir 229 280 Shahzad 236 Sharma, B.K. 237 285
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