@article{article_573972, title={The proximal point algorithm in complete geodesic spaces with negative curvature}, journal={Advances in the Theory of Nonlinear Analysis and its Application}, volume={3}, pages={192–200}, year={2019}, DOI={10.31197/atnaa.573972}, author={Kajimura, Takuto and Kimura, Yasunori}, keywords={CAT($-1$) space,proximal point algorithm,resolvent,convex function}, abstract={<div>The proximal point algorithm is an approximation method for finding a minimizer of a convex function. In this paper, we introduce the resolvent for a convex function in complete geodesic spaces with negative curvature. Using properties of the resolvent, we show the proximal point algorithm in complete geodesic spaces with negative curvature.  </div>}, number={4}, publisher={Erdal KARAPINAR}