@article { author = {Ranjbar, S.}, title = {W-convergence of the proximal point algorithm in complete CAT(0) metric spaces}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {43}, number = {3}, pages = {817-834}, year = {2017}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {‎In this paper‎, ‎we generalize the proximal point algorithm to complete CAT(0) spaces and show‎ ‎that the sequence generated by the proximal point algorithm‎ $w$-converges to a zero of the maximal‎ ‎monotone operator‎. ‎Also‎, ‎we prove that if $f‎: ‎X\rightarrow‎ ‎]-\infty‎, +‎\infty]$ is a proper‎, ‎convex and lower semicontinuous‎ ‎function on the complete CAT(0) space $X$‎, ‎then the proximal point algorithm $w$-converges to a zero of the subdifferential of $f$‎, ‎i.e., a minimizer of $f$‎. ‎Some strong convergence results (convergence in metric) are also presented with additional assumptions on the monotone operator and‎ ‎the convex function $f$.}, keywords = {Keywords: Hadamard space,maximal monotone operator,Proximal point algorithm,w-convergence,Subdifferential}, url = {http://bims.iranjournals.ir/article_971.html}, eprint = {http://bims.iranjournals.ir/article_971_82f5acff6dbe281bad8d1a4e7301a6f6.pdf} }