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The purpose of this paper is to study existence and approximation of solutions of system of variational inclusions involving multi-valued H-accretive and single-valued accretive operators over two different closed convex subsets of a Banach space. The convergence analysis of two proposed iteration processes for approximating solutions will be conducted within the conceptual framework of the ''altering point technique'' without uniform convexity of underlying spaces. This technique should make existing or new results in solving system of variational inequalities and variational inclusions. [ABSTRACT FROM AUTHOR]

We consider a new system of generalized variational inequalities (SGVI) defined on two closed convex subsets of a real Hilbert space. To find the solution of considered SGVI, a parallel Mann iteration process and a parallel S-iteration process have been proposed and the strong convergence of the sequences generated by these parallel iteration processes is discussed. Numerical example illustrates that the proposed parallel S-iteration process has an advantage over parallel Mann iteration process in computing altering points of some mappings. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of fixed points for a class of Lipschitzian type mappings and asymptotic pointwise Lipschitz type mappings in hyperbolic 2- uniformly convex metric spaces. In the same space setting, we deal the problem of approximation of fixed points via modified Mann iteration process. Our result generalizes and extends the corresponding results of Dehaish et al. [7], Goebel and Kirk [8], Kirk and Xu [18] and Sahu et al. [24] and many others in this direction. [ABSTRACT FROM AUTHOR]

The Mann iterates behave well for nonexpansive mappings for any initial guess in the domain. Our aim in this article is to extend this method to a broad class of inexact fixed point algorithms generated by nearly nonexpansive sequences in Banach spaces and to locate the weak limit of the iterates by its initial guesses. Due to the inexactness, our algorithms become efficiently applicable for a wider class of problems. As applications, we give convergence theorems for finding solutions of variational inclusion problems and constrained multiple-sets split feasibility problems. Our results are significant refinements and improvements of the corresponding results in the literature. [ABSTRACT FROM AUTHOR]

It is well known that the rate of convergence of 5-iteration process introduced by Agarwal et al. [J. Nonlinear Convex Anal., 8 (1) (2007), 61-79.] is faster than Picard iteration process for contraction operators. Following the ideas of S-iteration process, we introduce a parallel S-iteration process for finding altering points of nonlinear operators. We apply our algorithms to solve a system of operator equations in Banach space setting. This work also includes convergence analysis of hybrid steepest-descent-like method and hybrid Newton-like method in the context of altering points. [ABSTRACT FROM AUTHOR]

Let X be a real reflexive Banach space with a weakly continuous duality mapping Jφ. Let C be a nonemptyweakly closed star-shaped (with respect to u) subset of X. Let F= {T(t) : t ∊ [0, + ∞)} be a uniformly continuous semigroup of asymptotically nonexpansive self-mappings of C, which is uniformly continuous at zero. We will showthat the implicit iteration scheme: yn = αnu+(1-αn)T(tn)yn, for all n ∊ N, converges strongly to a common fixed point of the semigroup F for some suitably chosen parameters {αn} and {tn}. Our results extend and improve corresponding ones of Suzuki (2002), Xu (2005), and Zegeye and Shahzad (2009). [ABSTRACT FROM AUTHOR]

We study in this paper the existence and the approximation of solutions of variational inequalities involving generalized pseudocontractive mappings in Banach spaces. The convergence analysis of a proposed hybrid iterative method for approximating common zeros or fixed points of a possibly infinitely countable or uncountable family of such operators will be conducted within the conceptual framework of the "viscosity approximation technique" in reflexive Banach spaces with uniform Gâteaux differentiable norms. This technique should make existing or new results in solving variational inequalities more applicable. [ABSTRACT FROM AUTHOR]

In 1969, Kannan1 gave the definition of a new mapping which had presented a condition which is more lenient than contraction condition. The purpose of this note is to introduce K-Iterated Function System using Kannan mapping which will cover a larger range of mappings. We also prove the Collage theorem for the K-Iterated Function System. [ABSTRACT FROM AUTHOR]