CONVEX CONTRACTIONS OF ORDER <i>n</i> IN <i>CAT</i>(0) SPACES

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 C AT(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 C AT (0) spaces. Our results are new in C AT (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.

Journal

JORDAN JOURNAL OF MATHEMATICS AND STATISTICS

Year

2022

Volume

15

Issue

1

Pages

123-137

ISSN

2075-7905

eISSN

2227-5487

DOI

10.47013/15.1.9

WoS UID

WOS:000779274100009