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In this paper, we introduce and consider a new generalized system of nonlinear mixed variational inequality involving three difference relaxed cocoercive operators. This work is to use the resolvent operator technique to find the common solutions for a new generalized system of relaxed cocoercive mixed variational inequality problems and fixed point problems for Lipschitz mappings in Hilbert spaces. Our result in this paper improves and generalizes some know corresponding results in the literature. [ABSTRACT FROM AUTHOR]

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, we introduce a general iterative process for approximating common fixed point of two nonexpansive mappings in Banach spaces. We establish some strong convergence theorems of the general iteration scheme under some mild conditions. Our results improve and extend the corresponding results of many others form Hilbert spaces to Banach spaces. [ABSTRACT FROM AUTHOR]

Let (Ω, Σ) be a measurable space, χ a Banach space, C a weakly compact convex subset of X and T : Ω × C → C a random operator. We prove the random version of a deterministic fixed point theorem when τ is uniformly Lipschitzian random operators and satisfies property P such that σ(T(ω ·)) ≤ √WCS(χ) for all ω ε Ω, and T is asymptotically regular on C. Our results also give stochastic version generalization of some results of Domínguez Benavides and Xu [A new geometrical coefficient for Banach spaces and its applications in fixed point theory, Nonlinear Anal. 25 No. 3 (1995), 311-325.]. [ABSTRACT FROM AUTHOR]

Let (Ω, Ε) be a measurable space with Ε a ω-algebra of subset of Ω, X a separable Banach space, C a nonempty closed bounded convex subset of X and T : Ω × C → C a random operator. We prove the random version of a deterministic fixed point theorem when T is an asymptotically non-expansive random operator and X satisfy the uniform Opial's condition. Furthermore, we also prove that if T is an asymptotically nonexpansive random operator which satisfy the Maluta's constant D(X) < 1, and T is weakly random asymptotically regular on C. Then T has a random fixed point. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iterative scheme for finding the common element of the set of common fixed points of countable family of nonexpansive mappings, the set of solution of a mixed equilibrium problem and the set of solution of the variational inequality problems for a relaxed (u,v)-cocoercive and µ-Lipschitz continuous mapping in Hilbert spaces. We show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions. Our results improve and extend the recent ones announced by [Y.J. Cho, X.Q. Qin, M. Kang, Some results for equilibrium problems and fixed point problems in Hilbert spaces, J. Comput. Anal. Appl. 11(2009) 294-316] 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.], 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]