Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
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.
Czasopismo
Rocznik
Tom
Strony
331--340
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
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