Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ISHIKAWA ITERATIVE SEQUENCE WITH ERRORS FOR φ-STRONGLY ACCRETIVE OPERATORS

  • LI, YOUNG-JIN (Department of Mathematics Sun Yat-sen University)
  • Published : 2005.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, the iterative solution is studied for equation Tx = f with a uniformly continuous ${\varphi}$-strongly accretive operators in arbitrary real Banach spaces. Our results extend, generalize and improve the corresponding results obtained by Zeng [11].

Keywords

References

  1. C. E. Chidume, An approximation method for monotone Lipschitzian operators in Hilbert spaces, J. Aust. Math. Soc.(series A) 41 (1986), 59-63 https://doi.org/10.1017/S144678870002807X
  2. C. E. Chidume, The iterative solution of the equation f = x + Tx for a monotone operator T in $L^{p}$ space, J. Math. Anal. Appl. 116 (1986), 531-537 https://doi.org/10.1016/S0022-247X(86)80017-8
  3. C. E. Chidume and M. O. Osilike, Iterative solutions of nonlinear accretive oper- ator equations in arbitrary Banach spaces, Nonlinear Anal. 36(1999), 863-872 https://doi.org/10.1016/S0362-546X(97)00611-1
  4. C. E. Chidume, Nonlinear accretive and pseudo-contractive operator equations in Banach spaces, Nonlinear Anal. 31 (1998), 779-789 https://doi.org/10.1016/S0362-546X(97)00439-2
  5. C. E. Chidume and H. Zegeye, Approximation of the zeros of m-accretive operator, Nonlinear Anal. 37 (1999), 81-96 https://doi.org/10.1016/S0362-546X(98)00146-1
  6. C. E. Chidume, Iterative solution of $0\{in}$ Ax for an m-accretive operator A in certain Banach spaces, J. Math. Anal. Appl. 269 (2002), 421-430 https://doi.org/10.1016/S0022-247X(02)00015-X
  7. W. G. Dotson, An iterative process for nonlinear monotonic nonexpansive opera- tors in Hilbert space, Math. Comp. 32 (1978), 223-225 https://doi.org/10.2307/2006268
  8. T. Kato, Nonlinear semigroups and evolutions equations, J. Math. Soc. Japan. 19 (1967), 508-520 https://doi.org/10.2969/jmsj/01940508
  9. L. Liu, Ishikawa-type and Mann-type iterative process with errors for constructing solutions of nonlinear equations involving m-accretive operators in Banach spaces, Nonlinear Anal. 34 (1998), 307-317 https://doi.org/10.1016/S0362-546X(97)00579-8
  10. Z. Q. Liu, Y. G. Xu and Y. J. Cho, Iterative solution of nonlinear equations with $\phi$-strongly accretive operators, Arch. Math. 77 (2001), 508-516 https://doi.org/10.1007/PL00000524
  11. Z. Luchuan, Ishikawa type iterative sequences with errors for Lipschitzian $\varphi$strongly accretive operator equations in arbitrary Banach spaces, Numer. Math. J. Chinese Univ.(English Ser.) 11 (2002), 25-33
  12. R. H. Martin, Jr., A global existence theorem for autonomous differential equa- tions in Banach space, Proc. Amer. Math. Soc. 26 (1970), 307-314 https://doi.org/10.2307/2036395
  13. S. Reich, An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal. 2 (1978), 85-92 https://doi.org/10.1016/0362-546X(78)90044-5
  14. R. T. Rockafellar, Local boundedness of nonlinear, monotone operator, Michigan Math. J. 16 (1969), 397-407 https://doi.org/10.1307/mmj/1029000324
  15. Y. Xu, Ishikawa and Mann Iterative process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91-101 https://doi.org/10.1006/jmaa.1998.5987