Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT(0) Spaces

Suppose that K is a nonempty closed convex subset of a complete CAT(0) space X with the nearest point projection P from X onto K. Let T:K→X be a nonexpansive nonself mapping with F(T):={x∈K:Tx=x}≠∅. Suppose that {xn} is generated iteratively by x1∈K, xn+1=P((1−αn)xn⊕αnTP[(1−βn)xn⊕βnTxn]), n≥1, where {αn} and {βn} are real sequences in [ε,1−ε] for some ε∈(0,1). Then {xn}Δ-converges to some point x∗ in F(T). This is an analog of a result in Banach spaces of Shahzad (2005) and extends a result of Dhompongsa and Panyanak (2008) to the case of nonself mappings

Fixed Points for Multivalued Mappings in Uniformly Convex Metric Spaces

The purpose of this paper is to ensure the existence of fixed points for multivalued nonexpansive weakly inward nonself-mappings in uniformly convex metric spaces. This extends a result of Lim (1980) in Banach spaces. All results of Dhompongsa et al. (2005) and Chaoha and Phon-on (2006) are also extended

On Multivalued Nonexpansive Mappings in ℝ-Trees

The relationships between nonexpansive, weakly nonexpansive, *-nonexpansive, proximally nonexpansive, proximally continuous, almost lower semicontinuous, and ɛ-semicontinuous mappings in ℝ-trees are studied. Convergence theorems for the Ishikawa iteration processes are also discussed

The Jordan–von Neumann constants and fixed points for multivalued nonexpansive mappings

AbstractThe purpose of this paper is to study the existence of fixed points for nonexpansive multivalued mappings in a particular class of Banach spaces. Furthermore, we demonstrate a relationship between the weakly convergent sequence coefficient WCS(X) and the Jordan–von Neumann constant CNJ(X) of a Banach space X. Using this fact, we prove that if CNJ(X) is less than an appropriate positive number, then every multivalued nonexpansive mapping T:E→KC(E) has a fixed point where E is a nonempty weakly compact convex subset of a Banach space X, and KC(E) is the class of all nonempty compact convex subsets of E

On stationary points of nonexpansive set-valued mappings

In this paper we deal with stationary points (also known as endpoints) of nonexpansive set-valued mappings and show that the existence of such points under certain conditions follows as a consequence of the existence of approximate stationary sequences. In particular we provide abstract extensions of well-known fixed point theorems.Dirección General de Enseñanza SuperiorJunta de Andalucí