Kim, Jong-Kyu;Liu, Ze-Qing;Kang, Shin-Min

  • Published : 2004.04.01


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.


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


  1. J. Math. Anal. Appl. v.192 Iterative solution of nonlinear equations with strongly accretive operators
  2. J. Math. Anal. Appl. v.192 Ishikawa iteration process for nonlinear Lipschitz strongly accretive mappings
  3. Computers Math. Applic. v.33 Iterative process with errors to nonlinear φ-strongly accretive operator equations in arbitrary Banach spaces X.P.Ding
  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
  6. J. Math. Anal. Appl. v.56 Comments on two fixed point iteration methods B.E.Rhoades
  7. J. Math. Anal. Appl. v.224 Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations Y.Xu
  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
  9. Math. Nachr. v.153 On a theorem of C.E Chidume concerning the Iterative approximation of fixed points J.Schu
  10. Proc. Amer. Math. Soc. v.4 Mean value methods in iteration W.R.Mann
  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
  13. Proc. Amer. Math. Soc. v.99 Iterative approximation of fixed points of Lipschitz strictly pseudo-contractive mappings C.E.Chidume
  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
  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
  18. Nonliear Anal. TMA v.31 Nonlinear accretive and pseudo-contractive operator equations in Banach spaces
  19. J. Math. Soc v.19 Nonlinear semigroups and evolution equations T.Kato
  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
  21. Proc. Amer. Math. Soc, v.4 Mean value methods in iteration W.R.Mann
  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

Cited by

  1. Convergence theorem for the common solution for a finite family of ϕ-strongly accretive operator equations vol.217, pp.15, 2011,
  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,
  3. A three-step iterative scheme for solving nonlinear ϕ-strongly accretive operator equations in Banach spaces vol.2012, pp.1, 2012,