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Convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces

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Języki publikacji
EN
Abstrakty
EN
In this paper, we give some necessary and sufficient conditions for an implicit iteration process with errors for a finite family of asymptotically quasi-nonexpansive mappings converging to a common fixed of the mappings in convex metric spaces. Our results extend and improve some recent results of Sun, Wittmann, Xu and Ori, and Zhou and Chang.
Rocznik
Strony
331--340
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
  • Govt. Nagarjun P.G. College of Science Department of Mathematics & Information Technology, Raipur (Chhattisgarh), India, saluja_1963@rediffmail.com
Bibliografia
  • [1] S.S. Chang, J.K. Kim, Convergence theorems of the Ishikawa type iterative sequences with errors for generalized quasi-contractive mappings in convex metric spaces, Appl. Math. Lett. 16 (2003) 4, 535–542.
  • [2] S.S. Chang, J.K. Kim, D.S. Jin, Iterative sequences with errors for asymptotically quasi-nonexpansive type mappings in convex metric spaces, Arch. Inequal. Appl. 2 (2004), 365–374.
  • [3] S.S. Chang, On the approximating problem of fixed points for asymptotically nonexpansive mappings, Indian J. Pure Appl. Math. 32 (2001) 9, 1–11.
  • [4] J.K. Kim, K.H. Kim, K.S. Kim, Convergence theorems of modified three-step iterative sequences with mixed errors for asymptotically quasi-nonexpansive mappings in Banach spaces, Panamer. Math. J. 14 (2004) 1, 45–54.
  • [5] J.K. Kim, K.H. Kim, K.S. Kim, Three-step iterative sequences with errors for asymptotically quasi-nonexpansive mappings in convex metric spaces, Nonlinear Anal. Convex Anal. RIMS 1365 (2004), 156–165.
  • [6] Q.H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 259 (2001), 1–7.
  • [7] Q.H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings with error member, J. Math. Anal. Appl. 259 (2001), 18–24.
  • [8] Q.H. Liu, Iterative sequences for asymptotically quasi-nonexpansive mappings with error member of uniformly convex Banach spaces, J. Math. Anal. Appl. 266 (2002), 468–471.
  • [9] W.R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506–510.
  • [10] W.V. Petryshyn, T.E. Williamson, Strong and weak convergence of the sequence of successive approximations for quasi-nonexpansive mappings, J. Math. Anal. Appl. 43 (1973), 459–497.
  • [11] J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl. 158 (1991), 407–413.
  • [12] Z.H. Sun, Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003), 351–358.
  • [13] W. Takahashi, A convexity in metric space and nonexpansive mappings I, Kodai Math. Sem. Rep. 22 (1970), 142–149.
  • [14] K.K. Tan, H.K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), 301–308.
  • [15] R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992), 486-491.
  • [16] H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001), 767-773.
  • [17] Y. Zhou, S.S. Chang, Convergence of implicit iteration process for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim. 23 (2002) 7–8, 911–921.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHT-0003-0009
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