JOURNAL BROWSE
Search
Advanced SearchSearch Tips
NEW ITERATIVE PROCESS FOR THE EQUATION INVOLVING STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
NEW ITERATIVE PROCESS FOR THE EQUATION INVOLVING STRONGLY ACCRETIVE OPERATORS IN BANACH SPACES
Zeng, Ling-Yan; Li, Jun; Kim, Jong-Kyu;
  PDF(new window)
 Abstract
In this paper, under suitable conditions, we show that the new class of iterative process with errors introduced by Li et al converges strongly to the unique solution of the equation involving strongly accretive operators in real Banach spaces. Furthermore, we prove that it is equivalent to the classical Ishikawa iterative sequence with errors.
 Keywords
convergence;iterative process;strongly accretive operators;
 Language
English
 Cited by
 References
1.
R. P. Agarwal, N. J. Huang, and Y. J. Cho, Stability of iterative processes with errors for nonlinear equations of $\phi$-strongly accretive type operators, Numer. Funct. Anal. Optim. 22 (2001), no. 5-6, 471-485 crossref(new window)

2.
S. S. Chang, Some problems and results in the study of nonlinear analysis, Nonlinear Anal. 30 (1997), no. 7, 4197-4208 crossref(new window)

3.
S. S. Chang, On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces, J. Math. Anal. Appl. 216 (1997), no. 1, 94-111 crossref(new window)

4.
C. E. Chidume, An iterative process for nonlinear Lipschitzian strongly accretive map- pings in $L_p$ spaces, J. Math. Anal. Appl. 151 (1990), no. 2, 453-461 crossref(new window)

5.
Y. J. Cho, H. Zhou, and J. K. Kim, Iterative approximations of zeroes for accretive operators in Banach spaces, Commun. Korean Math. Soc. 21 (2006), no. 2, 237-251 crossref(new window)

6.
N. J. Huang, Y. J. Cho, B. S. Lee, and J. S. Jung, Convergence of iterative processes with errors for set-valued pseudocontractive and accretive type mappings in Banach spaces, Comput. Math. Appl. 40 (2000), no. 10-11, 1127-1139 crossref(new window)

7.
S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc. 44 (1974), 147-150 crossref(new window)

8.
J. K. Kim, Convergence of Ishikawa iterative sequences for accretive Lipschitzian map- pings in Banach spaces, Taiwanese J. Math. 10 (2006), no. 2, 553-561 crossref(new window)

9.
J. K. Kim, S. M. Jang, and Z. Liu, Convergence theorems and stability problems of Ishikawa iterative sequences for nonlinear operator equations of the accretive and strongly accretive operators, Comm. Appl. Nonlinear Anal. 10 (2003), no. 3, 85-98

10.
J. K. Kim, K. S. Kim, and Y. M. Nam, Convergence and stability of iterative processes for a pair of simultaneously asymptotically quasi-nonexpansive type mappings in convex metric spaces, J. Comput. Anal. Appl. 9 (2007), no. 2, 159-172

11.
J. K. Kim and Y. M. Nam, Modified Ishikawa iterative sequences with errors for asymp- totically set-valued pseudocontractive mappings in Banach spaces, Bull. Korean Math. Soc. 43 (2006), no. 4, 847-860 crossref(new window)

12.
J. Li, Inequalities on sequences with applications, Acta Math. Sinica (Chin. Ser.) 47 (2004), no. 2, 273-278

13.
J. Li, N. J. Huang, H. J. Hwang, and Y. J. Cho, Stability of iterative procedures with er- rors for approximating common fixed points of quasi-contractive mappings, Appl. Anal. 84 (2005), no. 3, 253-267 crossref(new window)

14.
L. S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accre- tive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995), no. 1, 114-125 crossref(new window)

15.
W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. 4 (1953), 506- 510 crossref(new window)

16.
R. H. Martin, A global existence theorem for autonomous differential equations in a Banach space, Proc. Amer. Math. Soc. 26 (1970), 307-314 crossref(new window)

17.
Y. G. Xu, Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), no. 1, 91-101 crossref(new window)