Search

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]

In this paper, we introduce and study the random nonlinear variational inclusion problem with multi-valued random operators. We define a random iterative algorithm for finding the approximate solutions of class of random variational inclusions and establish the convergence of random iterative sequence generated by proposed algorithm in a uniformly smooth Banach space. Our result in this paper improves and generalizes some know corresponding results in the literature. [ABSTRACT FROM AUTHOR]

In this paper is to introduce a new iterative scheme for finding solutions of a variational inequality for inverse-strongly accretive mappings with a viscosity approximation method in Banach spaces. We obtain a strong convergence theorem in Banach spaces under some parameters controlling conditions. Our results extend and improve the recent results of Yan Hao [Iterative algorithms for inverse-strongly accretive mappings with applications, J. Appl. Math. Comput., 31, 193-202, 2009.], YeoI Je Cho et al., [Strong convergence of an iterative algorithm for accretive operators in Banach spaces, J. Comput. Anal. and AppI., vol. 10, no. 1, 113-125, 2008.] and many others. [ABSTRACT FROM AUTHOR]

In this paper is to introduce a new iterative scheme for finding solutions of a variational inequality for inverse-strongly accretive mappings with a viscosity approximation method in Banach spaces. We obtain a strong convergence theorem in Banach spaces under some parameters controlling conditions. Our results extend and improve the recent results of Yan Hao [Iterative algorithms for inverse-strongly accretive mappings with applications, J. Appl. Math. Comput., 31, 193{202, 2009.], Yeol Je Cho et al., [Strong convergence of an iterative algorithm for accretive operators in Banach spaces, J. Comput. Anal. and Appl., vol. 10, no. 1, 113{125, 2008.] and many others. [ABSTRACT FROM AUTHOR]