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ITERATIVE APPROXIMATIONS OF ZEROES FOR ACCRETIVE OPERATORS IN BANACH SPACES
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 Title & Authors
ITERATIVE APPROXIMATIONS OF ZEROES FOR ACCRETIVE OPERATORS IN BANACH SPACES
Cho Yeol-Je; Zhou Haiyun; Kim Jong-Kyu;
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 Abstract
In this paper, we introduce and study a new iterative algorithm for approximating zeroes of accretive operators in Banach spaces.
 Keywords
reflexive Banach space;uniformly Gateuax differentiable norm;nonexpansive retract;iterative algorithm;fixed point;range condition;strong convergence;weak convergence;
 Language
English
 Cited by
1.
NEW ITERATIVE PROCESS FOR THE EQUATION INVOLVING STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES,;;;

대한수학회보, 2007. vol.44. 4, pp.861-870 crossref(new window)
 References
1.
H. Brezis and P. L. Lions, Produits infinis de resolvants, Israel J. Math. 29 (1978), 329-345 crossref(new window)

2.
F. E. Browder, Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660-665 crossref(new window)

3.
R. E. Bruck and G. B. Passty, Almost convergence of the infinite product of resolvents in Banach spaces, Nonlinear Anal. 3 (1979), 279-282 crossref(new window)

4.
R. E. Bruck and S. Reich, Nonexpansive projections and resolvents of accretive operators in Banach spaces, Houston J. Math. 3 (1977), 459-470

5.
B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967), 957-961 crossref(new window)

6.
J. S. Jung and W. Takahashi, Dual convergence theorems for the infinite products of resoluenis in Banach spaces, Kodai Math. J. 14 (1991), 358-364 crossref(new window)

7.
S. Kamimura, S. H. Khan and W. Takahashi, Iterative schemes for approximating solutions of relations involving accretive operators in Banach spaces, Fixed Point Theory and Applications, Vol. 5, Edited by Y. J. Cho, J. K. Kim and S. M. Kang, Nova Science Publishers, Inc., 2003, 41-52

8.
P. L. Lions, Une methode iterative de resolution d'une inequation variationnelle, Israel J. Math. 31 (1978), 204-208 crossref(new window)

9.
L. S. Liu, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995), 114-125 crossref(new window)

10.
W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510

11.
O. Nevanlinna and S. Reich, Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces, Israel J. Math. 32 (1979), 44-58 crossref(new window)

12.
Z. Opial, Weak convergence of the sequence of successive approximations for non expansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597 crossref(new window)

13.
A. Pazy, Remarks on nonlinear ergodic theory in Hilbert spaces, Nonlinear Anal. 6 (1979), 863-871

14.
S. Reich, On infinite products of resoluenis, Atti Acad. Naz. Lincei 63 (1977), 338-340

15.
S. Reich, Weak convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 67 (1979), 274-276 crossref(new window)

16.
S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980), 287-292 crossref(new window)

17.
R. T. Rockafellar , Monotone operators and the proximal point algorithm, SIAM J. Control and Optim. 14 (1976), 877-898 crossref(new window)

18.
W. Takahashi, Nonlinear Functional Analysis, Kindai-Kagaku-Sha, Tokyo, 1988

19.
W. Takahashi, Fixed point theorems and nonlinear ergodic theorems for nonlinear semigroups and their applications, Nonlinear Anal. 30 (1997), 1283-1293 crossref(new window)

20.
W. Takahashi, Nonlinear Analysis and Convex Analysis, Edited by W. Takahashi and T. Tanaka, World Scientific Publishing Company, 1999, p. 87-94

21.
W. Takahashi and G. E. Kim, Approximating fixed points of nonexpansive mappings in Banach spaces, Math. Japon. 48 (1998), 1-9

22.
W. Takahashi and Y. Ueda, On Reich's strong convergence theorems for resolve of accretive operators, J. Math. Anal. Appl. 104 (1984), 546-553 crossref(new window)