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Volumn 64, Issue 9, 2006, Pages 2022-2042

Iterative approaches to convex feasibility problems in Banach spaces

Author keywords

Banach space; Convex feasibility problem; Duality mapping; Iterative approach; Nonexpansive mapping; Sunny nonexpansive retraction

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; INTEGER PROGRAMMING; PROBLEM SOLVING;

EID: 33344472544     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.07.036     Document Type: Article
Times cited : (99)

References (34)
  • 1
    • 0030586523 scopus 로고    scopus 로고
    • The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space
    • H.H. Bauschke The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space J. Math. Anal. Appl. 202 1996 150 159
    • (1996) J. Math. Anal. Appl. , vol.202 , pp. 150-159
    • Bauschke, H.H.1
  • 2
    • 0030246542 scopus 로고    scopus 로고
    • On projection algorithms for solving convex feasibility problems
    • H.H. Bauschke, and J.M. Borwein On projection algorithms for solving convex feasibility problems SIAM Rev. 38 1996 1367 1426
    • (1996) SIAM Rev. , vol.38 , pp. 1367-1426
    • Bauschke, H.H.1    Borwein, J.M.2
  • 3
    • 0002728205 scopus 로고
    • Convergence of approximants to fixed points of nonexpansive non-linear mappings in Banach spaces
    • F.E. Browder Convergence of approximants to fixed points of nonexpansive non-linear mappings in Banach spaces Arch. Ration. Mech. Anal. 24 1967 82 90
    • (1967) Arch. Ration. Mech. Anal. , vol.24 , pp. 82-90
    • Browder, F.E.1
  • 4
    • 84972558718 scopus 로고
    • Nonexpansive projections on subsets of Banach spaces
    • R.E. Bruck Nonexpansive projections on subsets of Banach spaces Pac. J. Math. 47 1973 341 355
    • (1973) Pac. J. Math. , vol.47 , pp. 341-355
    • Bruck, R.E.1
  • 5
    • 33646983265 scopus 로고
    • On the convex approximation property and the asymptotic behaviour of nonlinear contractions in Banach spaces
    • R.E. Bruck On the convex approximation property and the asymptotic behaviour of nonlinear contractions in Banach spaces Isr. J. Math. 38 1981 304 314
    • (1981) Isr. J. Math. , vol.38 , pp. 304-314
    • Bruck, R.E.1
  • 8
    • 77954607855 scopus 로고    scopus 로고
    • The convex feasibility problem in image recovery
    • P. Hawkes Academic Press New York
    • P.L. Combettes The convex feasibility problem in image recovery P. Hawkes Advances in Imaging and Electron Physics vol. 95 1996 Academic Press New York 155 270
    • (1996) Advances in Imaging and Electron Physics , vol.95 , pp. 155-270
    • Combettes, P.L.1
  • 9
    • 0031148181 scopus 로고    scopus 로고
    • Hilbertian convex feasibility problem: Convergence of projection methods
    • P.L. Combettes Hilbertian convex feasibility problem convergence of projection methods Appl. Math. Optim. 35 1997 311 330
    • (1997) Appl. Math. Optim. , vol.35 , pp. 311-330
    • Combettes, P.L.1
  • 10
    • 0009150796 scopus 로고
    • Viewing parallel projection methods as sequential ones in convex feasibility problems
    • G. Crombez Viewing parallel projection methods as sequential ones in convex feasibility problems Trans. Am. Math. Soc. 347 1995 2575 2583
    • (1995) Trans. Am. Math. Soc. , vol.347 , pp. 2575-2583
    • Crombez, G.1
  • 11
    • 0343456142 scopus 로고
    • Finding projections onto the intersection of convex sets in Hilbert spaces
    • G. Crombez Finding projections onto the intersection of convex sets in Hilbert spaces Numer. Funct. Anal. Optim. 16 1995 637 652
    • (1995) Numer. Funct. Anal. Optim. , vol.16 , pp. 637-652
    • Crombez, G.1
  • 12
    • 0031999680 scopus 로고    scopus 로고
    • Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings
    • F. Deutsch, and I. Yamada Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings Numer. Funct. Anal. Optim. 19 1998 33 56
    • (1998) Numer. Funct. Anal. Optim. , vol.19 , pp. 33-56
    • Deutsch, F.1    Yamada, I.2
  • 13
    • 0003317987 scopus 로고
    • Geometry of Banach spaces-selected topics
    • Springer Berlin
    • J. Diestel Geometry of Banach spaces-selected topics Lecture Notes in Mathematics vol. 485 1975 Springer Berlin
    • (1975) Lecture Notes in Mathematics , vol.485
    • Diestel, J.1
  • 14
    • 0003263852 scopus 로고
    • Topics in metric fixed point theory
    • Cambridge University Press Cambridge
    • K. Goebel, and W.A. Kirk Topics in metric fixed point theory Cambridge Studies in Advanced Mathematics vol. 28 1990 Cambridge University Press Cambridge
    • (1990) Cambridge Studies in Advanced Mathematics , vol.28
    • Goebel, K.1    Kirk, W.A.2
  • 16
    • 84894234564 scopus 로고
    • Fixed points of nonexpanding maps
    • B. Halpern Fixed points of nonexpanding maps Bull. Am. Math. Soc. 73 1967 957 961
    • (1967) Bull. Am. Math. Soc. , vol.73 , pp. 957-961
    • Halpern, B.1
  • 17
    • 0007687503 scopus 로고
    • Image restoration by a novel method of parallel projection onto constraint sets
    • T. Kotzer, N. Cohen, and J. Shamir Image restoration by a novel method of parallel projection onto constraint sets Opt. Lett. 20 1995 1172 1174
    • (1995) Opt. Lett. , vol.20 , pp. 1172-1174
    • Kotzer, T.1    Cohen, N.2    Shamir, J.3
  • 18
    • 0000736540 scopus 로고
    • Applications of serial- and parallel-projection methods to correlation filter design
    • T. Kotzer, N. Cohen, and J. Shamir Applications of serial- and parallel-projection methods to correlation filter design Appl. Opt. 34 1995 3883 3895
    • (1995) Appl. Opt. , vol.34 , pp. 3883-3895
    • Kotzer, T.1    Cohen, N.2    Shamir, J.3
  • 19
    • 0000222831 scopus 로고
    • Fixed point theorems for asymptotically nonexpansive mappings
    • T.C. Lim, and H.K. Xu Fixed point theorems for asymptotically nonexpansive mappings Nonlinear Anal. 22 1994 1345 1355
    • (1994) Nonlinear Anal. , vol.22 , pp. 1345-1355
    • Lim, T.C.1    Xu, H.K.2
  • 20
    • 0000736340 scopus 로고
    • Approximation de points fixes de contractions
    • P.L. Lions Approximation de points fixes de contractions C.R. Acad. Sci. Sèr. A-B Paris 284 1977 1357 1359
    • (1977) C.R. Acad. Sci. Sèr. A-B Paris , vol.284 , pp. 1357-1359
    • Lions, P.L.1
  • 21
    • 0042128551 scopus 로고    scopus 로고
    • Iterative approaches to finding nearest common fixed point of nonexpansive mappings in Hilbert spaces
    • J.G. O'Hara, P. Pillay, and H.K. Xu Iterative approaches to finding nearest common fixed point of nonexpansive mappings in Hilbert spaces Nonlinear Anal. 54 2003 1417 1426
    • (2003) Nonlinear Anal. , vol.54 , pp. 1417-1426
    • O'Hara, J.G.1    Pillay, P.2    Xu, H.K.3
  • 22
    • 0009119332 scopus 로고
    • Asymptotic behavior of contractions in Banach spaces
    • S. Reich Asymptotic behavior of contractions in Banach spaces J. Math. Anal. Appl. 44 1973 57 70
    • (1973) J. Math. Anal. Appl. , vol.44 , pp. 57-70
    • Reich, S.1
  • 23
    • 0043200261 scopus 로고
    • Some fixed point problems
    • S. Reich Some fixed point problems Atti Accad. Naz. Lincei 57 1974 194 198
    • (1974) Atti Accad. Naz. Lincei , vol.57 , pp. 194-198
    • Reich, S.1
  • 24
    • 33745998912 scopus 로고
    • Strong convergence theorems for resolvents of accretive operators in Banach spaces
    • S. Reich Strong convergence theorems for resolvents of accretive operators in Banach spaces J. Math. Anal. Appl. 75 1980 287 292
    • (1980) J. Math. Anal. Appl. , vol.75 , pp. 287-292
    • Reich, S.1
  • 25
    • 0001000182 scopus 로고
    • Some problems and results in fixed point theory
    • S. Reich Some problems and results in fixed point theory Contemp. Math. 21 1983 179 187
    • (1983) Contemp. Math. , vol.21 , pp. 179-187
    • Reich, S.1
  • 26
    • 0001896374 scopus 로고
    • Approximating fixed points of nonexpansive mappings
    • S. Reich Approximating fixed points of nonexpansive mappings Panam. Math. J. 4 2 1994 23 28
    • (1994) Panam. Math. J. , vol.4 , Issue.2 , pp. 23-28
    • Reich, S.1
  • 27
    • 0003388852 scopus 로고
    • Application of convex projection theory to image recovery in tomography and related areas
    • H. Stark Academic Press Orlando
    • M.I. Sezan, and H. Stark Application of convex projection theory to image recovery in tomography and related areas H. Stark Image Recovery Theory and Applications 1987 Academic Press Orlando 415 462
    • (1987) Image Recovery: Theory and Applications , pp. 415-462
    • Sezan, M.I.1    Stark, H.2
  • 28
    • 0031172967 scopus 로고    scopus 로고
    • Strong convergence to common fixed points of families of nonexpansive mappings
    • T. Shimizu, and W. Takahashi Strong convergence to common fixed points of families of nonexpansive mappings J. Math. Anal. Appl. 211 1997 71 83
    • (1997) J. Math. Anal. Appl. , vol.211 , pp. 71-83
    • Shimizu, T.1    Takahashi, W.2
  • 29
    • 21944452074 scopus 로고    scopus 로고
    • Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
    • N. Shioji, and W. Takahashi Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces Proc. Am. Math. Soc. 125 1997 3641 3645
    • (1997) Proc. Am. Math. Soc. , vol.125 , pp. 3641-3645
    • Shioji, N.1    Takahashi, W.2
  • 30
    • 0001682125 scopus 로고
    • Approximation of fixed points of nonexpansive mappings
    • R. Wittmann Approximation of fixed points of nonexpansive mappings Arch. Math. 58 1992 486 491
    • (1992) Arch. Math. , vol.58 , pp. 486-491
    • Wittmann, R.1
  • 31
    • 0036692463 scopus 로고    scopus 로고
    • Iterative algorithms for nonlinear operators
    • H.K. Xu Iterative algorithms for nonlinear operators J. London Math. Soc. 66 2002 240 256
    • (2002) J. London Math. Soc. , vol.66 , pp. 240-256
    • Xu, H.K.1
  • 32
    • 0037269525 scopus 로고    scopus 로고
    • An iterative approach to quadratic optimization
    • H.K. Xu An iterative approach to quadratic optimization J. Optim. Theory Appl. 116 3 2003 659 678
    • (2003) J. Optim. Theory Appl. , vol.116 , Issue.3 , pp. 659-678
    • Xu, H.K.1
  • 33
    • 0032002260 scopus 로고    scopus 로고
    • Quadratic approximation of fixed points of nonexpansive mappings in Hilbert spaces
    • I. Yamada, N. Ogura, Y. Yamashita, and K. Sakaniwa Quadratic approximation of fixed points of nonexpansive mappings in Hilbert spaces Numer. Funct. Anal. Optim. 19 1998 165 190
    • (1998) Numer. Funct. Anal. Optim. , vol.19 , pp. 165-190
    • Yamada, I.1    Ogura, N.2    Yamashita, Y.3    Sakaniwa, K.4
  • 34
    • 0020191832 scopus 로고
    • Image restoration by the method of convex projections: Part i - Theory
    • D.C. Youla, and H. Webb Image restoration by the method of convex projections Part I - Theory IEEE Trans. Med. Imaging MI-1 1982 81 94
    • (1982) IEEE Trans. Med. Imaging , vol.MI-1 , pp. 81-94
    • Youla, D.C.1    Webb, H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.