In this paper, a general system of variational inclusions in Banach Spaces is introduced. An iterative method for finding solutions of a general system of variational inclusions with inverse-strongly accretive mappings and common set of fixed points for a λ-strict pseudocontraction is established. Under certain conditions, by forward-backward splitting method, we prove strong convergence theore...

Let A + B be the pointwise (Minkowski) sum of two convex subsets A and B of a Banach space. Is it true that every continuous mapping h : X → A + B splits into a sum h = f + g of continuous mappings f : X → A and g : X → B? We study this question within a wider framework of splitting techniques of continuous selections. Existence of splittings is guaranteed by hereditary invertibility of linear ...

Abstract In this paper, we study the Ishikawa type iteration process with errors, which converges to a common fixed point of a pair of mappings in complete generalized convex metric spaces. Furthermore, we obtain the corresponding results in Banach spaces. Our result improve and generalize a recent result of Khan[S.H. Khan, Common fixed points of two quasi-contractive operators in normed spaces...

We introduce the concept of λ-hyperconvexity in metric spaces, generalizing the classical notion of a hyperconvex metric space. We show that a bounded metric space which is λ-hyperconvex has the fixed point property for nonexpansive mappings provided λ < 2. Uniformly convex Banach spaces are examples of such λ-hyperconvex spaces for some λ < 2. We furthermore investigate the relationship betwee...

The iterative schemes with some control conditions for a family of finite nonexpansive mappings are established in a Banach space. The main theorem improves results of Jung and Kim (also Bauschke). Our results also improve the corresponding results of Cho et al., Shioji and Takahashi, Xu, and Zhou et al. in certain Banach spaces and of Lions, O’Hara et al., and Wittmann in a framework of a Hilb...

It is shown that if X is a Banach space and C is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets {Ci : 1≤ i≤ n} of X , and each Ci has the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping of C has a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach...

The convex feasibility problem CFP of finding a point in the nonempty intersection ⋂N i 1Ci is considered, where N 1 is an integer and the Ci’s are assumed to be convex closed subsets of a Banach space E. By using hybrid iterative methods, we prove theorems on the strong convergence to a common fixed point for a finite family of relatively nonexpansive mappings. Then, we apply our results for s...

Let E be a real Banach Space and K a nonempty closed convex (not necessarily bounded) subset of E. Iterative methods for the approximation of fixed points of asymptotically demicontractive mappings T : K → K are constructed using the more general modified Mann and Ishikawa iteration methods with errors. Our results show that a recent result of Osilike [3] (which is itself a generalization of a ...

Let X be a Banach space. Let K be a nonempty subset of X. Let T : K → K be an I-asymptotically quasi-nonexpansive type mapping and I : K → K be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an I-asymptotically quasi-nonexpansive type ma...