Third International Conference on Applications of Mathematics to Nonlinear Sciences. Electron. J. Diff. Eqns., conf. 27 (2024), pp. 13-26. Title: Convergence theorems of implicit type iterations in geodesic spaces with negative curvature Authors: Yasunori Kimura (Toho Univ., Funabashi, Chiba, Japan) Kazuya Sasaki (Toho Univ., Funabashi, Chiba, Japan) Kakeru Torii (Japan) Abstract: In this article, we prove convergence theorems of the implicit iterative methods in the sense of Browder type and Xu-Ori type with (-1)-convex combination in CAT(-1) spaces. Published August 20, 2024. Math Subject Classifications: 47H09. Key Words: Geodesic space; convergence theorem; $\Delta$-convergence; CAT(-1) space