DOI QR코드

DOI QR Code

NECESSARY AND SUFFICIENT CONDITIONS FOR CONVERGENCE OF ISHIKAWA ITERATIVE SCHEMES WITH ERRORS TO φ-HEMICONTRACTIVE MAPPINGS

Liu, Seqing;Kim, Jong-Kyu;Kang, Shin-Min

  • Published : 2003.04.01

Abstract

The purpose of this paper is to establish the necessary and sufficient conditions which ensure the strong convergence of the Ishikawa iterative schemes with errors to the unique fixed point of a $\Phi$-hemicontractive mapping defined on a nonempty convex subset of a normed linear space. The results of this paper extend substantially most of the recent results.

Keywords

${\Phi}$-hemicontractive mapping;strongly pseudocontractive mapping;${\Phi}$-strongly pseudocontractive mapping;strictly hemicontractive mapping;Ishikawa iterative scheme with errors

References

  1. Applicable Anal. v.27 Fixed point iterations for certain classes of nonlinear mappings C.E.Chidume https://doi.org/10.1080/00036818808839722
  2. Proc. Amer. Math. Soc. v.44 Fixed point by a new iteration method S.Ishikawa https://doi.org/10.2307/2039245
  3. J. Math. Anal. appl. v.224 Iterative approaximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces S.S.Chang;Y.J.Cho;B.S.Lee;S.M.Kang https://doi.org/10.1006/jmaa.1998.5993
  4. J. Math. Anal. Appl. v.288 Convergence theorems for strictly psudo-contractive and strongly accretrive maps C.E.Chidume
  5. Proc. Amer. Math. Soc. v.125 Approximation of fixed points of a strictly psedocontractive mapping L.W.Liu https://doi.org/10.1090/S0002-9939-97-03858-6
  6. Numer. Funct. Anal. Optimiz. v.15 Fixed point iterations for strictly hemicontractive maps in uniformly smooth Banach spaces C.E.Chidume;M.O.Osilike https://doi.org/10.1080/01630569408816593
  7. J. Math. Anal. Appl. v.178 Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces K.K.Tan;H.K.Xu https://doi.org/10.1006/jmaa.1993.1287
  8. Proc. Amer. Math. Soc. v.120 Approximation of fixed points of strongly pseudo-contractive mappings C.E.Chidume https://doi.org/10.2307/2159893
  9. J. Math. Anal. Appl. v.192 Ishikawa iteration process for onlinear Lipschitz strongly accretive mappings C.E.Chidume;M.O.Osilike https://doi.org/10.1006/jmaa.1995.1200
  10. J. Math. Anal. Appl. v.194 Ishikawa and Mann iterative process with errors for nonlinear storngly accretive mappings in Banach spaces L.S.Liu https://doi.org/10.1006/jmaa.1995.1289
  11. J. Math. Anal. Appl. v.224 Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations Y.XU https://doi.org/10.1006/jmaa.1998.5987
  12. Nonlinear Anal. T. M. A. v.26 Iterative solutions of nonlinear equations in smooth Banach spaces C.E.Chidume https://doi.org/10.1016/0362-546X(94)00368-R
  13. Proc. Amer. Math. Soc. v.26 Mean value methods in iteration W.R.Mann
  14. Proc. Amer. Math. Soc. v.99 Iterative approaximation of fixed point of Lipschitz strictly pseu-doccontractive mappings C.E.Chidume https://doi.org/10.2307/2046626
  15. Nonlinear Anal. v.36 Iterative solution of nonlinear accretive operator equations in arbitrary Banach spaces C.E.Chidume;M.O.Osilike https://doi.org/10.1016/S0362-546X(97)00611-1
  16. Math. Nachr. v.153 On a theorem of C. E. Chidume concerning the iterative approximaton of fixed points J.Schu https://doi.org/10.1002/mana.19911530127
  17. J. Math. Soc. Japan v.19 Nonlinear semigroups and evolution equations T.Kato https://doi.org/10.2969/jmsj/01940508
  18. J. Math. Anal. Appl. v.192 Iterative solutions of nonlinear equations with strongly accretive operators C.E.Chidume https://doi.org/10.1006/jmaa.1995.1185
  19. J. Math. Anal. Appl. v.200 Iterative solution of nonlinear equations of Ø-storngly accretive type M.O.osilike https://doi.org/10.1006/jmaa.1996.0203
  20. J. Korean Math. Soc. v.36 Ishikawa and Mann iterative processes with errors for nonlinear $\phi$-strongly quasi-accretive mappings in normed linear spaces H.Y.zhou;Y.J.Cho
  21. Nonlinear Anal. v.30 Some problems and results in the study of nonlinear analysis S.S.Chang https://doi.org/10.1016/S0362-546X(97)00388-X

Cited by

  1. Implicit iteration scheme for two phi-hemicontractive operators in arbitrary Banach spaces vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-521