Viscosity approximations with weak contraction for finding a common solution of fixed points and a general system of variational inequalities for two accretive operators
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Publication Details
Author list: Kumam P., Katchang P.
Publisher: Eudoxus Press LLC
Publication year: 2012
Journal: Journal of Computational Analysis and Applications (1521-1398)
Volume number: 14
Issue number: 7
Start page: 1269
End page: 1287
Number of pages: 19
ISSN: 1521-1398
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we prove a strong convergence theorem for finding a common solutions of a general system of variational inequalities involving two difierent 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. ฉ 2012 EUDOXU1S26 P9RESS, LLC.
Keywords
General system of variational inequalities, Modi-fied viscosity extragradient approximation method