CONVERGENCE OF AN IMPLICIT ITERATIVE PROCESS FOR TWO FINITE FAMILIES OF NONEXPANSIVE MAPPINGS

  • Cho, S.Y. (Department of Mathematics Gyeongsang National University) ;
  • Kang, S.M. (Department of Mathematics and RINS Gyeongsang National University) ;
  • Qin, X. (Department of Mathematics Hangzhou Normal University) ;
  • Kwun, Y.C. (Department of Mathematics Dong-A University)
  • 투고 : 2010.05.18
  • 심사 : 2010.08.19
  • 발행 : 2010.09.30

초록

Convergence of an implicit iterative process is investigated for nonexpansive mappings. Strong and weak convergence theorems of common fixed points of two finite families of nonexpansive mappings are established in the framework of Banach spaces.

키워드

과제정보

연구 과제 주관 기관 : Dong-A University

참고문헌

  1. F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Natl. Acad. Sci. USA 54 (1965), 1041-1044. https://doi.org/10.1073/pnas.54.4.1041
  2. F. E. Browder, Semicontractive and semiaccretive nonlinear mappings in Ba- nach spaces, Bull. Amer. Math. Soc. 74 (1968), 660-665. https://doi.org/10.1090/S0002-9904-1968-11983-4
  3. C. E. Chidume and N. Shahzad, Strong convergence of an implicit iteration pro- cess for a finite family of nonexpansive mappings, Nonlinear Anal. 62 (2005), 1149-1156. https://doi.org/10.1016/j.na.2005.05.002
  4. D. van Dulst, Equivalent norms and the fixed point property for nonexpansive mapping, J. Lond. Math. Soc. 25 (1982), 139-144. https://doi.org/10.1112/jlms/s2-25.1.139
  5. J. G. Falset, W. Kaczor, T. Kuczumow and S. Reich, Weak convergence the- orems for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 43 (2001), 377-401. https://doi.org/10.1016/S0362-546X(99)00200-X
  6. Y. Hao, S. Y. Cho and X. Qin, Some weak convergence theorems for a family of asymptotically nonexpansive nonself mappings, Fixed Point Theory Appl. 2010 (2010), Article ID 218573.
  7. Z. Opial, Weak convergence of the sequence of successive appproximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597. https://doi.org/10.1090/S0002-9904-1967-11761-0
  8. S. Reich, Weak convergence theorems for nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 67 (1979), 274-276. https://doi.org/10.1016/0022-247X(79)90024-6
  9. B. E. Rhoades and S. M. Soltuz, The convergence of mean value iteration for a family of maps, Int. J. Math. Math. Sci. 2005 (2005), 3479-3485. https://doi.org/10.1155/IJMMS.2005.3479
  10. K. K. Tan and H. K. Xu, Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl. 178 (1993), 301-308. https://doi.org/10.1006/jmaa.1993.1309
  11. S. Thianwan and S. Suantai, Weak and strong convergence of an implicity iteration process for a finite family of nonexpansive mappings, Sci. Math. Jpn. 66 (2007), 221-229.
  12. H. K. Xu and M. G. Ori, An implicit iterative process for nonexpansive map- pings, Numer. Funct. Anal. Optim. 22 (2001), 767-773. https://doi.org/10.1081/NFA-100105317