Browse > Article
http://dx.doi.org/10.4134/CKMS.2005.20.1.071

ISHIKAWA ITERATIVE SEQUENCE WITH ERRORS FOR φ-STRONGLY ACCRETIVE OPERATORS  

LI, YOUNG-JIN (Department of Mathematics Sun Yat-sen University)
Publication Information
Communications of the Korean Mathematical Society / v.20, no.1, 2005 , pp. 71-78 More about this Journal
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
Ishikawa iterative sequences with errors; duality mapping; Banach space;
Citations & Related Records
연도 인용수 순위
  • Reference
1 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   DOI   ScienceOn
2 C. E. Chidume, Nonlinear accretive and pseudo-contractive operator equations in Banach spaces, Nonlinear Anal. 31 (1998), 779-789   DOI   ScienceOn
3 C. E. Chidume and H. Zegeye, Approximation of the zeros of m-accretive operator, Nonlinear Anal. 37 (1999), 81-96   DOI   ScienceOn
4 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   DOI   ScienceOn
5 W. G. Dotson, An iterative process for nonlinear monotonic nonexpansive opera- tors in Hilbert space, Math. Comp. 32 (1978), 223-225   DOI
6 T. Kato, Nonlinear semigroups and evolutions equations, J. Math. Soc. Japan. 19 (1967), 508-520   DOI
7 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   DOI   ScienceOn
8 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   DOI   ScienceOn
9 C. E. Chidume, An approximation method for monotone Lipschitzian operators in Hilbert spaces, J. Aust. Math. Soc.(series A) 41 (1986), 59-63   DOI
10 R. H. Martin, Jr., A global existence theorem for autonomous differential equa- tions in Banach space, Proc. Amer. Math. Soc. 26 (1970), 307-314   DOI
11 S. Reich, An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal. 2 (1978), 85-92   DOI   ScienceOn
12 R. T. Rockafellar, Local boundedness of nonlinear, monotone operator, Michigan Math. J. 16 (1969), 397-407   DOI
13 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
14 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   DOI
15 Y. Xu, Ishikawa and Mann Iterative process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91-101   DOI   ScienceOn