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On iterative convergence of resolvents of acceretive operators

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Języki publikacji
EN
Abstrakty
EN
Weak and strong convergence of resolvents of accretive operators have been studied in this paper under different iteration schemes. In particular for an accretive operator A, the inclusion 0 Ax has been solved. Applying this result, we have found the solution of equation x + Bx = f where B is a Lipschitzian accretive operator.
Wydawca
Rocznik
Strony
407--417
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
  • Faculty of Engineering Sciences, GIK Institute of Engineering Sciences and Technology, Topi, Swabi, N.W.F.P, Pakistan
Bibliografia
  • [1] H. Brézis and P. L. Lions, Produits infinis de resolvants, Israel J. Math.,29 (1978), 329-345.
  • [2] F. E. Browder, Nonlinear mappings of nonexpansive and accretive type in Banach Spaces, Bull. Amer. Math. Soc. 73 (1967), 875-882.
  • [3] R. E. Bruck and G. B. Passty, Almost convergence of the infinite product of resolvents in Banach spaces, Nonlinear Anal., 3 (1979), 279-282.
  • [4] R. E. Bruck and S. Reich, Nonexpansive projections and resolvents of accretive operators in Banach spaces, Houston J. Math. 3 (1977), 459-470.
  • [5] B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc., 73 (1967), 957-961.
  • [6] J. S. Jung and W. Takahashi, Dual convergence theorems for the infinite product of resolvents in Banach spaces, Kodai Math. J., 14 (1991), 358-364.
  • [7] P. L. Lions, Une methode iterative de resolution d'une inequation variationnelle, Israel J. Math., 31 (1978), 204-208.
  • [8] W. R. Mann, Mean value methods in iterations, Proc. Amer. Math. Soc., 4 (1953), 506-510.
  • [9] Z. Opial, Weak convergence of sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), 591-597.
  • [10] A. Pazy, Remarks on nonlinear ergodic theory in Hilbert spaces, Nonlinear Anal., 6 (1979), 863-871.
  • [11] R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J., Control and Optimization, 14 (1976), 877-898.
  • [12] J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc., 43 (1991), 153-159.
  • [13] W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, Japan, 2000.
  • [14] W. Takahashi and Y. Ueda, On Reich's strong convergence theorems for resolvents of accretive operators, J. Math. Anal. Appl., 104 (1984), 546-553.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0010-0016
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