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Strong convergence of an implicit iteration process for a finite family of quasi-contractive operators

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Języki publikacji
EN
Abstrakty
EN
The purpose of this paper is to establish a strong convergence of an implicit iteration process to a common fixed point for a finite family of quasi-contractive operators. Our theorems give an armative response to a question raised by [Xu and Ori, Numer. Funct. Anal. Optim. 22 (2001) 767-773 ].
Wydawca
Rocznik
Strony
203--208
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
  • Department of Mathematics Comsats Institute of Information Technology Islamabad, Pakistan 30, H-8/1, arafiq@comsats.edu.pk
Bibliografia
  • [1] V. Berinde, On the convergence of Mann iteration for a class of quasi-contractive operators, Preprint, 2003.
  • [2] V. Berinde, On the convergence of the Ishikawa iteration in the class of quasi contractive operators, Acta Math Univ. Comenianae, LXXIII 1 (2004), 119-126.
  • [3] V. Berinde, A convergence theorem for some mean value fixed point iteration procedures, Demonstratio Math. 38 (1) (2005), 177-184.
  • [4] H. H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl. 202 (1996), 150-159.
  • [5] S. K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci. 25 (1972), 727-730.
  • [6] C. E. Chidume and N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Analysis (TMA) 62 (2005) 1149-1156.
  • [7] L. B. Ciric, A generalization of Banach principle, Proc. Amer. Math. Soc. 45 (1974), 727-730.
  • [8] B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967), 957-961.
  • [9] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 10 (1968), 71-76.
  • [10] R. Kannan, Some results on fixed points III , Fund. Math. 70 (1971), 169-177.
  • [11] R. Kannan, Construction of fixed points of class of nonlinear mappings, J. Math. Anal. Appl. 41 (1973), 430-438.
  • [12] P. L. Lions, Approximations de points fixes de contractions, C. R. Acad. Sci. Paris, Ser. A, 284 (1977), 1357-1359.
  • [13] S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980), 287-292.
  • [14] R.Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992), 399-404.
  • [15] H. K. Xu, R. Ori, An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001) 767-773.
  • [16] T. Zamfirescu, Fixed point theorems in metric spaces, Arch. Math. (Basel) 23 (1972), 292-298.
  • [17] Y. Zhou and S. S. Chang, Convergence of implicit iteration process for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Appl. 23 (2002) 911-921.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0033-0020
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