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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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42 167 129 166 173 174 3 3 (c)- 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 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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