In this paper, we work with the notion of the measure of nonhyperconvexity introduced by Cianciaruso and De Pascale [6] in order to obtain new fixed-point theorems in hyperconvex metric spaces. This class of metric spaces was introduced by Aronszajn and Panitchpakdi [1] in 1956 to study problems on extension of uniformly continuous mappings. Several and interesting properties of these spaces we...

The influence of fixed point theorems for contractive and nonexpansive mappings see 1, 2 on fixed point theory is so huge that there are many results dealing with fixed points of mappings satisfying various types of contractive and nonexpansive conditions. On the other hand, it is also huge that well-known Brouwer’s and Schauder’s fixed point theorems for set-contractive mappings exert an influ...

Using the implicit iteration and the hybrid method in mathematical programming, we prove weak and strong convergence theorems for finding common fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Our results include many convergence theorems by Xu and Ori 2001 and Zhang and Su 2007 as special cases. We also apply our method to find a common element to the set o...

We prove a strong convergence theorem for finding a common element of the set of solutions for generalized equilibrium problems, the set of fixed points of a relatively nonexpansive mapping, and the set of fixed points of a quasi-φ-nonexpansive mapping in a Banach space by using the shrinking Projection method. Our results improve the main results in S. Takahashi and W. Takahashi 2008 and Takah...

We introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings andmonotone mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of set of fixed points of nonexpansive mapping and the set of solutions of variational inequality for an inversestrongly monotone mappings, whic...

and Applied Analysis 3 Let E be a real Banach space and let C be a nonempty closed and convex subset of E, and A : C → E∗ be a mapping. The classical variational inequality problem for a mapping A is to find x∗ ∈ C such that 〈 Ax∗, y − x∗〉 ≥ 0, ∀y ∈ C. 1.7 The set of solutions of 1.4 is denoted by VI A,C . Recall that A is called i monotone if 〈 Ax −Ay, x − y〉 ≥ 0, ∀x, y ∈ C, 1.8 ii an α-invers...

In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditi...

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...

In this article, we deal with iterative methods for approximation of fixed points and their applications. We first discuss fixed point theorems for a nonexpansive mapping or a family of nonexpansive mappings. In particular, we state a fixed point theorem which answered affirmatively a problem posed during the Conference on Fixed Point Theory and Applications held at CIRM, Marseille-Luminy, 1989...

and Applied Analysis 3 It is clear that 1.7 is equivalent to 〈 Sx − Sy, x − y ≤ ∥x − y∥2, ∀x, y ∈ C. 1.8 The class of κ-strict pseudocontractions which was introduced by Browder and Petryshyn 17 in 1967 has been considered by many authors. It is easy to see that the class of strict pseudocontractions falls into the one between the class of nonexpansive mappings and the class of pseudocontractio...