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http://dx.doi.org/10.7858/eamj.2011.27.1.011

VISCOSITY METHODS OF APPROXIMATION FOR A COMMON SOLUTION OF A FINITE FAMILY OF ACCRETIVE OPERATORS  

Chen, Jun-Min (College of Mathematics and Computer Hebei University)
Zhang, Li-Juan (College of Mathematics and Computer Hebei University)
Fan, Tie-Gang (College of Mathematics and Computer Hebei University)
Publication Information
East Asian mathematical journal / v.27, no.1, 2011 , pp. 11-21 More about this Journal
Abstract
In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.
Keywords
Viscosity method; accretive operator; resolvent operator; weakly continuous duality mapping;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Paul-Emile Mainge, Viscosity methods for zeros of accretive operators, J. Approximation Theory 140 (2006), 127-140.   DOI   ScienceOn
2 Suziki T., Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces, Fixed Point Theory Appl. 1 (2005), 103-123.
3 Takahashi W., Nonlinear Function Analysis-Fixed Point Theory and its Applications, Yokohama Publishers, Yokohama, 2000 (in Japanese).
4 Xu H. K., An iterative approach to quadratic optimization, J. Optim. Theory Appl. 116 (2003), 659-678.   DOI   ScienceOn
5 Xu H. K., Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004), 279-291.   DOI   ScienceOn
6 Zegeye H. and Shahzad N., Strong convergence theorems for a common zero of a family of m-accretive mappings, Nonlinear Anal. 66 (2007), 1161-1169.   DOI   ScienceOn
7 Browder F. E., Convergence theorems or sequences of nonlinear operators in Banach space, Math. Z. 100 (1967), 202-225.
8 Ciovenescu I., Geometry of Banach space, Duality Mapping and Nonlinear Problems, Kluner Academic Publishers, 1990.
9 Chen Junmin, Zhang Lijuan and Fan Tiegang, Viscosity Approximation Methods for Nonexpansive Mappings and Monotone Mappings, J. Math. Anal. Appl. 334 (2007), 1450-1461.   DOI   ScienceOn
10 Gossez J. P. and Lami Dozo E., Some geometric properties related to the fixed point theory for nonexpansive mappings, Pacific J. Math. 40 (1972), 565-573.   DOI
11 Hu Lianggen and Liu Liwei, A new iterative algorithm for common solutions of a finite family of accretive operators, Nonlinear Anal. 70 (2009), 2344-2351.   DOI   ScienceOn
12 Moudafi A., Viscosity Approximation Methods for Fixed-Points Problems, J. Math. Anal. Appl. 241 (2000), 46-55.   DOI   ScienceOn
13 Jung J. S., Strong convergence of an iterative method for finding common zeros of a finite family of accretive operators, Commun. Korean Math. Soc. 24(3) (2009), 381-393.   DOI