Endpoints of multivalued nonexpansive mappings in geodesic spaces
نویسنده
چکیده
Let X be either a uniformly convex Banach space or a reflexive Banach space having the Opial property. It is shown that a multivalued nonexpansive mapping on a bounded closed convex subset of X has an endpoint if and only if it has the approximate endpoint property. This is the first result regarding the existence of endpoints for such kind of mappings even in Hilbert spaces. The related result in a complete CAT(0) space is also given.
منابع مشابه
Geodesic metric spaces and generalized nonexpansive multivalued mappings
In this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in CAT(0) spaces as well as in UCED Banach spaces. Moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...
متن کاملGeodesic Metric Spaces and Generalized Nonexpansive Multivalued Mappings
In this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in CAT(0) spaces as well as in UCED Banach spaces. Moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...
متن کاملCommon fixed points of a finite family of multivalued quasi-nonexpansive mappings in uniformly convex Banach spaces
In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.
متن کاملComposition of resolvents and quasi-nonexpansive multivalued mappings in Hadamared spaces
The proximal point algorithm, which is a well-known tool for finding minima of convex functions, is generalized from the classical Hilbert space framework into a nonlinear setting, namely, geodesic metric spaces of nonpositive curvature. In this paper we propose an iterative algorithm for finding the common element of the minimizers of a finite family of convex functions a...
متن کاملEndpoints of generalized $phi$-contractive multivalued mappings of integral type
Recently, some researchers have established some results on existence of endpoints for multivalued mappings. In particular, Mohammadi and Rezapour's [Endpoints of Suzuki type quasi-contractive multifunctions, U.P.B. Sci. Bull., Series A, 2015] used the technique of $alpha-psi$-contractive mappings, due to Samet et al. (2012), to give some results about endpoints of Suzuki type quasi-contractiv...
متن کامل