Abstract
We introduce a new composite iterative scheme to approximate a zero of an m-accretive operator A defined on uniform smooth Banach spaces and a reflexive Banach space having a weakly continuous duality map. It is shown that the iterative process in each case converges strongly to a zero of A. The results presented in this paper substantially improve and extend the results due to Ceng et al. [L.C. Ceng, H.K. Xu, J.C. Yao, Strong convergence of a hybrid viscosity approximation method with perturbed mappings for nonexpansive and accretive operators, Taiwanese J. Math. (in press)], Kim and Xu [T.H. Kim, H.K. Xu, Strong convergence of modified Mann iterations, Nonlinear Anal. 61 (2005) 51-60] and Xu [H.K. Xu, Strong convergence of an iterative method for nonexpansive and accretive operators, J. Math. Anal. Appl. 314 (2006) 631-643]. Our work provides a new approach for the construction of a zero of m-accretive operators.
| Original language | English |
|---|---|
| Pages (from-to) | 1830-1840 |
| Number of pages | 11 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 70 |
| Issue number | 5 |
| DOIs | |
| State | Published - 1 Mar 2009 |
Bibliographical note
Funding Information:In this research, the second and third authors were supported by a KFUPM Funded Research Project # IN070362.
Keywords
- Composite iterative scheme
- Uniformly smooth
- Weakly continuous duality map
- Zero of an operator
- m-accretive operator
ASJC Scopus subject areas
- Analysis
- Applied Mathematics