DOI QR코드

DOI QR Code

ALMOST STABILITY OF ISHIKAWA ITERATIVE SCHEMES WITH ERRORS FOR φ-STRONGLY QUASI-ACCRETIVE AND φ-HEMICONTRACTIVE OPERATORS

  • Kim, Jong-Kyu (Department of Mathematics Kyungnam University) ;
  • Liu, Ze-Qing (Department of Mathematics Liaoning Normal University) ;
  • Kang, Shin-Min (Department of Mathematics Gyeongsang National University)
  • Published : 2004.04.01

Abstract

In this paper, we establish almost stability of Ishikawa iterative schemes with errors for the classes of Lipschitz $\phi$-strongly quasi-accretive operators and Lipschitz $\phi$-hemicontractive operators in arbitrary Banach spaces. The results of this paper extend a few well-known recent results.

Keywords

Ishikawa iterative scheme with errors;$\phi$-strongly quasiaccretive operator;$\phi$-hemicontractive operator;almost stability

References

  1. J. Math. Anal. Appl. v.192 Iterative solution of nonlinear equations with strongly accretive operators https://doi.org/10.1006/jmaa.1995.1185
  2. J. Math. Anal. Appl. v.192 Ishikawa iteration process for nonlinear Lipschitz strongly accretive mappings https://doi.org/10.1006/jmaa.1995.1200
  3. Computers Math. Applic. v.33 Iterative process with errors to nonlinear φ-strongly accretive operator equations in arbitrary Banach spaces X.P.Ding https://doi.org/10.1016/S0898-1221(97)00055-2
  4. Parallel and Sci. Compu v.9 Convergence and stability of the Ishikawa iteration procedure with errors for nonlinear equations of the φ-strongly accretive type Z.Liu;S.M.Kang
  5. Nonlinear Anal. v.36 Iterative solution of nonlinear φ-strongly accertive operator equations in arbitrary Banach spaces https://doi.org/10.1016/S0362-546X(97)00566-X
  6. J. Math. Anal. Appl. v.56 Comments on two fixed point iteration methods B.E.Rhoades https://doi.org/10.1016/0022-247X(76)90038-X
  7. 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
  8. 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
  9. Math. Nachr. v.153 On a theorem of C.E Chidume concerning the Iterative approximation of fixed points J.Schu https://doi.org/10.1002/mana.19911530127
  10. Proc. Amer. Math. Soc. v.4 Mean value methods in iteration W.R.Mann https://doi.org/10.2307/2032162
  11. Math. Japon. v.33 A stable interation procedure for nonexpansive mappings A.M.Harder;T.L.Hicks
  12. Nonlinear Anal. TMA v.26 Iterative solutions of nonlinear equations in smooth Banach spaces https://doi.org/10.1016/0362-546X(94)00368-R
  13. Proc. Amer. Math. Soc. v.99 Iterative approximation of fixed points of Lipschitz strictly pseudo-contractive mappings C.E.Chidume https://doi.org/10.2307/2046626
  14. Math. Jappon. v.33 Stability results for fixed point iteration procedures
  15. Proc. Amer. Math. Soc, v.44 Fixed point by a new iteration procedures S.Ishikawa https://doi.org/10.2307/2039245
  16. Fixed points theory and stability results for fixed point iteration procudures,Ph.D. Thesis A.M.Harder
  17. Proc. Amer. Math. Soc, v.125 Approximation of fixed points of a strictly pseudocontractive mapping L.W.Liu https://doi.org/10.1090/S0002-9939-97-03858-6
  18. Nonliear Anal. TMA v.31 Nonlinear accretive and pseudo-contractive operator equations in Banach spaces https://doi.org/10.1016/S0362-546X(97)00439-2
  19. J. Math. Soc v.19 Nonlinear semigroups and evolution equations T.Kato https://doi.org/10.2969/jmsj/01940508
  20. 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
  21. Proc. Amer. Math. Soc, v.4 Mean value methods in iteration W.R.Mann https://doi.org/10.1006/jmaa.1996.0203
  22. J. Math. anal. Appl. v.227 Stability of the Mann and Ishikawa iteration procedure for φ-strong pseudocontractions and nonlinear equation of the φ-strongly accertive type https://doi.org/10.1006/jmaa.1998.6075

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  2. Convergence of SP iterative scheme with mixed errors for accretive Lipschitzian and strongly accretive Lipschitzian operators in Banach spaces vol.90, pp.9, 2013, https://doi.org/10.1080/00207160.2013.765558
  3. A three-step iterative scheme for solving nonlinear ϕ-strongly accretive operator equations in Banach spaces vol.2012, pp.1, 2012, https://doi.org/10.1186/1687-1812-2012-149