Convex Contractions of order n In CAT(0) Spaces

Abstract

In this paper, we work on convex contraction of order n. Our first result in general metric spaces shows that each convex contraction of order n is a Bessaga mapping. We then turn our attention to CAT (0) spaces. We prove a demiclosedness principle for such mappings in this setting. Next, we consider modified Mann iteration process and prove some convergence theorems for fixed points of such mappings in CAT (0) spaces. Our results are new in CAT (0) setting. Our results remain true in linear spaces like Hilbert and Banach spaces. Finally, we give an example in order to support our main results and to demonstrate the efficiency of modified Mann iteration process.

Key words and phrases. Convex contraction of order n, modified Mann iteration scheme, CAT (0) space, convergence, fixed point.

2000 Mathematics Subject Classification. 47H10, 49M15, 65K10