DOI QR코드

DOI QR Code

CONVERGENCE THEOREMS FOR ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPS

  • Osilike, M.O. (Department of Mathematics, University of Nigeria) ;
  • Igbokwe, D.I. (Department of Mathematics, University of Nigeria)
  • Published : 2002.08.01

Abstract

We prove that the results of Chang, Park and Cho in [1] concerning the iterative approximation of asymptotically pseudocontractive maps with bounded ranges can be extended to a certain class of asymptotically pseudocontractive maps whose ranges need not be bounded.

References

  1. Bull. Korean Math. Soc. v.37 no.1 Iterative approximations of fixed points of asymptotically nonexpansive mappings in Banach spaces S. S. Chang;J. Y. Park;Y. J. Cho
  2. Computers and Math. Applic. v.37 Mann and Ishikawa iterations with errors for asymptotically nonexpansive mappings Z. Huang
  3. J. Math. Soc. Japan v.19 Nonlinear semigroups and evolution equations T. Kato https://doi.org/10.2969/jmsj/01940508
  4. J. Math. Anal. Appl. v.194 Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces L. S. Liu https://doi.org/10.1006/jmaa.1995.1289
  5. Indian J. Pure Appl. Math. v.29 no.12 Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings M. O. Osilike
  6. J. Mathematical and Computer Modelling v.32 Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings M. O. Osilike;S. C. Aniagbosor https://doi.org/10.1016/S0895-7177(00)00199-0
  7. Nonlinear Analysis v.26 no.11 Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings L. Qihou https://doi.org/10.1016/0362-546X(94)00351-H
  8. J. Math. Anal. Appl. v.183 Fixed point iteration for certain nonlinear mappings B. E. Rhoades https://doi.org/10.1006/jmaa.1994.1135
  9. J. Math. Anal. Appl. v.158 Iterative construction of fixed points of asymptotically nonexpansive mappings J. Schu https://doi.org/10.1016/0022-247X(91)90245-U
  10. Bull. Austral. Math. Soc. v.43 Weak and strong convergence of fixed points of asymptotically nonexpansive mappings J. Schu https://doi.org/10.1017/S0004972700028884
  11. Proc. Amer. Math. Soc. v.122 no.3 Fixed point iteration processes for asymptotically nonexpansive mappings K-K. Tan;H-K. Xu https://doi.org/10.1090/S0002-9939-1994-1203993-5
  12. J. Math. Anal. Appl. v.178 Approximating fixed point of nonexpansive mappings by the Ishikawa iteration process K-K. Tan;H-K. Xu https://doi.org/10.1006/jmaa.1993.1309
  13. J. Math. Anal. Appl. v.224 Ishikawa and Mann iterative methods with errors for nonlinear accretive operator equations Y. Xu https://doi.org/10.1006/jmaa.1998.5987

Cited by

  1. Strong convergence of a CQ method for k-strictly asymptotically pseudocontractive mappings vol.2012, pp.1, 2012, https://doi.org/10.1186/1687-1812-2012-208