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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 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]