International Journal of Analysis and Applications | 2026
Authors: Artsawang N.; Suanoom C.; Gebrie A.G.
DOI: 10.28924/2291-8639-24-2026-42
Journal: International Journal of Analysis and Applications
Year: 2026
Publisher: Etamaths Publishing
Document Type: Article
Open Access: All Open Access; Gold Open Access
Cited by: 0
In this paper, we present a new fixed point theorem for mappings defined on complete CAT(0) spaces. Specifically, we introduce an enhanced version of the Suzuki-type interpolative Reich–RusČirić contraction that incorporates a geodesic iteration condition reflecting the nonpositive curvature structure of CAT(0) spaces. Our main result ensures the existence and uniqueness of a fixed point under suitable contractive conditions and orbital admissibility. The proof relies heavily on the convexity properties of the metric in CAT(0) spaces and the geometrical behavior of iterative sequences along geodesics. This contributes to the ongoing development of fixed point theory in nonlinear and curved metric settings. © 2026 the author(s).
CAT(0) spaces; fixed point; interpolative contraction; Reich-Rus-Cirić type mappings