메뉴 건너뛰기




Volumn 29, Issue 3-4, 2008, Pages 304-323

Stable convergence theorems for infinite products and powers of nonexpansive mappings

Author keywords

Amalgamated operators method; Complete metric space; Convex feasibility problem; Fixed point; Infinite product; Weak ergodic theorem

Indexed keywords

ALGEBRA;

EID: 46249089856     PISSN: 01630563     EISSN: 15322467     Source Type: Journal    
DOI: 10.1080/01630560801998161     Document Type: Article
Times cited : (53)

References (28)
  • 2
    • 0030246542 scopus 로고    scopus 로고
    • On projection algorithms for solving convex feasibility problems
    • H.H. Bauschke and J.M. Borwein (1996). On projection algorithms for solving convex feasibility problems. SIAM Rev. 38:367-426.
    • (1996) SIAM Rev , vol.38 , pp. 367-426
    • Bauschke, H.H.1    Borwein, J.M.2
  • 3
    • 0002351732 scopus 로고    scopus 로고
    • The method of cyclic projections for closed convex sets in Hilbert space
    • Recent Dev. Optimiz. Theory Nonlinear Anal
    • H.H. Bauschke, J.M. Borwein, and A.S. Lewis (1997). The method of cyclic projections for closed convex sets in Hilbert space. In Recent Dev. Optimiz. Theory Nonlinear Anal., Vol. 204. Contemp. Math. Series, pp. 1-38.
    • (1997) Contemp. Math. Series , vol.204 , pp. 1-38
    • Bauschke, H.H.1    Borwein, J.M.2    Lewis, A.S.3
  • 4
    • 0000256894 scopus 로고
    • Nonexpansive projections and resolvents of accretive operators in Banach spaces
    • R.E. Bruck and S. Reich (1977). Nonexpansive projections and resolvents of accretive operators in Banach spaces. Houston J. Math. 3:459-470.
    • (1977) Houston J. Math , vol.3 , pp. 459-470
    • Bruck, R.E.1    Reich, S.2
  • 5
    • 39449105966 scopus 로고    scopus 로고
    • D. Butnariu, R. Davidi, G.T. Herman, and I.G. Kazantsev (2007). Stable convergence behavior of projection methods for convex feasibility and optimization problems. IEEE J. Selected Topics Signal Processing 1:540-547.
    • D. Butnariu, R. Davidi, G.T. Herman, and I.G. Kazantsev (2007). Stable convergence behavior of projection methods for convex feasibility and optimization problems. IEEE J. Selected Topics Signal Processing 1:540-547.
  • 6
    • 39449117883 scopus 로고    scopus 로고
    • Convergence to fixed points of inexact orbits of Bregman-monotone and of nonexpansive operators in Banach spaces
    • Yokahama Publishers, Yokahama, pp
    • D. Butnariu, S. Reich, and A.J. Zaslavski (2006). Convergence to fixed points of inexact orbits of Bregman-monotone and of nonexpansive operators in Banach spaces. Fixed Point Theory and Its Applications. Yokahama Publishers, Yokahama, pp. 11-32.
    • (2006) Fixed Point Theory and Its Applications , pp. 11-32
    • Butnariu, D.1    Reich, S.2    Zaslavski, A.J.3
  • 9
    • 0001054069 scopus 로고
    • Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari.
    • G. Cimmino (1938). Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari. La Ricerca Scientifica (Roma) 9:326-333.
    • (1938) La Ricerca Scientifica (Roma) , vol.9 , pp. 326-333
    • Cimmino, G.1
  • 10
    • 0035251770 scopus 로고    scopus 로고
    • On the numerical robustness of a parallel projection method in signal synthesis
    • P.L. Combettes (2001). On the numerical robustness of a parallel projection method in signal synthesis. IEEE Signal Processing Lett. 8:45-47.
    • (2001) IEEE Signal Processing Lett , vol.8 , pp. 45-47
    • Combettes, P.L.1
  • 11
    • 84966230219 scopus 로고
    • Ergodic theorems in demography
    • J.E. Cohen (1979). Ergodic theorems in demography. Bull. Am. Math. Soc. 1:275-295.
    • (1979) Bull. Am. Math. Soc , vol.1 , pp. 275-295
    • Cohen, J.E.1
  • 12
    • 0039756214 scopus 로고
    • A parallel projection method for finding a common point of a family of convex sets
    • A.R. De Pierro and A.N. Iusem (1985). A parallel projection method for finding a common point of a family of convex sets. Pesquisa Operacional 5:1-20.
    • (1985) Pesquisa Operacional , vol.5 , pp. 1-20
    • De Pierro, A.R.1    Iusem, A.N.2
  • 13
    • 0000274159 scopus 로고    scopus 로고
    • Convergence of unrestricted products of nonexpansive mappings in spaces with the Opial property
    • J. Dye, T. Kuczumow, P.K. Lin, and S. Reich (1996). Convergence of unrestricted products of nonexpansive mappings in spaces with the Opial property. Nonlinear Anal. 26:767-773.
    • (1996) Nonlinear Anal , vol.26 , pp. 767-773
    • Dye, J.1    Kuczumow, T.2    Lin, P.K.3    Reich, S.4
  • 15
    • 0000927821 scopus 로고
    • Asymptotic properties for inhomogeneous iterations of nonlinear operators
    • T. Fujimoto and U. Krause (1988). Asymptotic properties for inhomogeneous iterations of nonlinear operators. SIAM J. Math. Anal. 19:841-853.
    • (1988) SIAM J. Math. Anal , vol.19 , pp. 841-853
    • Fujimoto, T.1    Krause, U.2
  • 16
    • 0347466422 scopus 로고    scopus 로고
    • Classical Theory of Nonexpansive Mappings
    • Kluwer, Dordrecht, pp
    • K. Goebel and W.A. Kirk (2001). Classical Theory of Nonexpansive Mappings. Handbook of Metric Fixed Point Theory, Kluwer, Dordrecht, pp. 49-91.
    • (2001) Handbook of Metric Fixed Point Theory , pp. 49-91
    • Goebel, K.1    Kirk, W.A.2
  • 18
    • 0001684890 scopus 로고
    • Unrestricted products of contractions in Banach spaces
    • P.K. Lin (1995). Unrestricted products of contractions in Banach spaces, Nonlinear Anal. 24:1103-1108.
    • (1995) Nonlinear Anal , vol.24 , pp. 1103-1108
    • Lin, P.K.1
  • 19
    • 51249185817 scopus 로고
    • Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces
    • O. Nevanlinna and S. Reich (1979). Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces. Israel J. Math. 32:44-58.
    • (1979) Israel J. Math , vol.32 , pp. 44-58
    • Nevanlinna, O.1    Reich, S.2
  • 21
    • 0000036624 scopus 로고
    • Some nonlinear weak ergodic theorems
    • R.D. Nussbaum (1990). Some nonlinear weak ergodic theorems. SIAM J. Math. Anal. 21:436-460.
    • (1990) SIAM J. Math. Anal , vol.21 , pp. 436-460
    • Nussbaum, R.D.1
  • 22
    • 84968481460 scopus 로고
    • Weak convergence of the sequence of successive approximations for nonexpansive mappings
    • Z. Opial (1967). Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull. Am. Math. Soc. 73:591-597.
    • (1967) Bull. Am. Math. Soc , vol.73 , pp. 591-597
    • Opial, Z.1
  • 23
    • 0345903723 scopus 로고
    • The round-off stability of iterations
    • A.M. Ostrowski (1967). The round-off stability of iterations. Z. Angew. Math. Mech. 47:77-81.
    • (1967) Z. Angew. Math. Mech , vol.47 , pp. 77-81
    • Ostrowski, A.M.1
  • 25
    • 0033148224 scopus 로고    scopus 로고
    • Convergence of generic infinite products of nonexpansive and uniformly continuous operators
    • S. Reich and A.J. Zaslavski (1999). Convergence of generic infinite products of nonexpansive and uniformly continuous operators. Nonlinear Anal. 36:1049-1065.
    • (1999) Nonlinear Anal , vol.36 , pp. 1049-1065
    • Reich, S.1    Zaslavski, A.J.2
  • 26
    • 33846033958 scopus 로고    scopus 로고
    • Generic convergence of infinite products of nonexpansive mappings in Banach and hyperbolic spaces
    • Optimization and Related Topics A. Rubinov and B. Glover, eds, Kluwer, Dordrecht, pp
    • S. Reich and A.J. Zaslavski (2001). Generic convergence of infinite products of nonexpansive mappings in Banach and hyperbolic spaces. In Optimization and Related Topics (A. Rubinov and B. Glover, eds.), Applied Optimization Series, Vol. 47. Kluwer, Dordrecht, pp. 371-402.
    • (2001) Applied Optimization Series , vol.47 , pp. 371-402
    • Reich, S.1    Zaslavski, A.J.2
  • 27
    • 0001363448 scopus 로고
    • On rings of operators. Reduction Theory
    • J. Von Neumann (1949). On rings of operators. Reduction Theory. Ann. Math. 50:401-485.
    • (1949) Ann. Math , vol.50 , pp. 401-485
    • Von Neumann, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.