DOI QR코드

DOI QR Code

STRONG CONVERGENCE OF AN IMPLICIT ITERATIVE PROCESS FOR AN INFINITE FAMILY OF STRICT PSEUDOCONTRACTIONS

  • Cho, Yeol-Je (DEPARTMENT OF MATHEMATICS EDUCATION AND RINS GYEONGSANG NATIONAL UNIVERSITY) ;
  • Kang, Shin-Min (DEPARTMENT OF MATHEMATICS AND RINS GYEONGSANG NATIONAL UNIVERSITY) ;
  • Qin, Xiaolong (DEPARTMENT OF MATHEMATICS HANGZHOU NORMAL UNIVERSITY)
  • Received : 2009.04.24
  • Published : 2010.11.30

Abstract

In this paper, we consider an implicit iterative process with errors for an in nite family of strict pseudocontractions. Strong convergence theorems are established in the framework of Banach spaces. The results presented in this paper improve and extend the recent ones announced by many others.

Keywords

implicit iterative process;strict pseudocontraction;nonexpansive mapping;common fixed point;Banach space

Acknowledgement

Supported by : Korea Research Foundation

References

  1. F. E. Browder and W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197-228. https://doi.org/10.1016/0022-247X(67)90085-6
  2. R. Chen, Y. Song, and H. Zhou, Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings, J. Math. Anal. Appl. 314 (2006), no. 2, 701-709. https://doi.org/10.1016/j.jmaa.2005.04.018
  3. C. E. Chidume and N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62 (2005), no. 6, 1149-1156. https://doi.org/10.1016/j.na.2005.05.002
  4. K. Deimling, Zeros of accretive operators, Manuscripta Math. 13 (1974), 365-374. https://doi.org/10.1007/BF01171148
  5. M. O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004), no. 1, 73-81. https://doi.org/10.1016/j.jmaa.2004.01.038
  6. S. Plubtieng, K. Ungchittrakool, and R. Wangkeeree, Implicit iterations of two finite families for nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim. 28 (2007), no. 5-6, 737-749. https://doi.org/10.1080/01630560701348525
  7. X. Qin, Y. J. Cho, and M. Shang, Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings, Appl. Math. Comput. 210 (2009), no. 2, 542-550. https://doi.org/10.1016/j.amc.2009.01.018
  8. X. Qin, Y. Su, and M. Shang, On the convergence of strictly pseudo-contractive map-pings in Banach spaces, J. Prime Res. Math. 3 (2007), 154-161.
  9. N. Shahzad and H. Zegeye, Strong convergence of an implicit iteration process for a finite family of generalized asymptotically quasi-nonexpansive maps, Appl. Math. Comput. 189 (2007), no. 2, 1058-1065. https://doi.org/10.1016/j.amc.2006.11.152
  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), no. 2, 301-308. https://doi.org/10.1006/jmaa.1993.1309
  11. S. Thianwan and S. Suantai, Weak and strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Sci. Math. Jpn. 66 (2007), no. 1, 73-81.
  12. H. K. Xu and R. G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001), no. 5-6, 767-773. https://doi.org/10.1081/NFA-100105317
  13. L. C. Zeng and J. C. Yao, Implicit iteration scheme with perturbed mapping for common fixed points of a finite family of nonexpansive mappings, Nonlinear Anal. 64 (2006), no. 11, 2507-2515. https://doi.org/10.1016/j.na.2005.08.028
  14. H. Zhou, Convergence theorems of common fixed points for a finite family of Lipschitz pseudocontractions in Banach spaces, Nonlinear Anal. 68 (2008), no. 10, 2977-2983. https://doi.org/10.1016/j.na.2007.02.041

Cited by

  1. Strong Convergence Theorems of Modified Ishikawa Iterative Method for an Infinite Family of Strict Pseudocontractions in Banach Spaces vol.2011, 2011, https://doi.org/10.1155/2011/549364
  2. A General Iterative Method for a Nonexpansive Semigroup in Banach Spaces with Gauge Functions vol.2012, 2012, https://doi.org/10.1155/2012/506976
  3. Strong convergence theorems for uniformly L-Lipschitzian asymptotically pseudocontractive mappings in Banach spaces vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-79
  4. Strong and weak convergence theorems for general mixed equilibrium problems and variational inequality problems and fixed point problems in Hilbert spaces vol.247, 2013, https://doi.org/10.1016/j.cam.2013.01.004
  5. Implicit and Explicit Iterations with Meir-Keeler-Type Contraction for a Finite Family of Nonexpansive Semigroups in Banach Spaces vol.2012, 2012, https://doi.org/10.1155/2012/720192
  6. Hybrid algorithm for generalized mixed equilibrium problems and variational inequality problems and fixed point problems vol.62, pp.12, 2011, https://doi.org/10.1016/j.camwa.2011.10.068
  7. On Mann-type iteration method for a family of hemicontractive mappings in Hilbert spaces vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-41