Endpoint theorems for some generalized nonexpansive mappings in uniformly convex hyperbolic spaces

Abstract

The endpoint theory is one of the most important concepts which lies between the concept of xed points for single-valued mappings and the concept of xed points for multivalued mappings. The purpose of this thesis is to study the endpoint theory for some classes of multivalued mappings. We divided into three main parts. In the rst part, we study common endpoint theorems for a pair of single-valued Suzuki mapping and multivalued Suzuki mapping in a uniformly convex hyperbolic space. In the second part, we extend the concept of the (CN) inequality of Bruhat and Tits in a CAT(0) space to the general setting of a 2-uniformly convex hyperbolic space. Subsequently, we apply such inequality to prove the Δ and strong convergence of the Ishikawa iteration process for multivalued Suzuki mappings. Finally, in the last part, we use the notion of diametrically regular multivalued mappings, which is weaker than the endpoint condition to prove Browder's convergence theorem.