Fixed points for total asymptotically nonexpansive mappings in a new version of bead space
Abdolrahman Razani · International journal of industrial mathematics. · 2014
The notion of a bead metric space is dened as a nice generalization of the uniformly convex normed space such as CAT (0) space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, we dene a new version of bead space and called it CN -bead space. Then the existence of xed point for asymptotically nonexpansive mapping and total asymptotically nonexpansive mapping in CN -bead space are proved. In other word, Let K be a bounded subset of complete CN -bead space X. Then the xed point set F (T ), where T is a total asymptotically nonexpansive selfmap on K , is nonempty and closed. Moreover, the xed point set F (T ), where T is an asymptotically nonexpansive selfmap on K , is nonempty.