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Viscosity approximations with weak contraction for finding a common solution of fixed points and a general system of variational inequalities for two accretive operators.
- Source :
-
Journal of Computational Analysis & Applications . Nov2012, Vol. 14 Issue 7, p1269-1287. 19p. - Publication Year :
- 2012
-
Abstract
- In this paper, we prove a strong convergence theorem for finding a common solutions of a general system of variational inequalities involving two different inverse-strongly accretive operators and solutions of fixed point problems involving the nonexpansive mapping in a Banach space by using a modified viscosity extragradient method with weak contraction. Moreover, using the above results, we can apply to finding solutions of zeros of accretive operators and the class of k-strictly pseudocontractive mappings. The results presented in this paper extend and improve the corresponding results of Qin et al. [Convergence of an iterative algorithm for systems of variational inequalities and nonexpansive mappings with applications, J. Comput. Appl. Math., 233 (2009), 231-240.], Aoyama et al. [Weak convergence of an iterative sequence for accretive operators in Banach spaces, Fixed Point Theory and Applications, vol. 2006, Article ID 35390, 1-13.], Yao et al. [Modified extragradient methods for a system of variational inequalities in Banach spaces, Acta. Appl. Math., 110(3) (2010), 1211-1224.], Katchang et al. [A viscosity iterative scheme for inverse-strongly accretive operators in Banach spaces, Journal of Computational Analysis and Applications, 12(3) (2010), 678 686.] and many others. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15211398
- Volume :
- 14
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 73509923