Journal
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
Volume 49, Issue 1, Pages 399-408Publisher
HACETTEPE UNIV, FAC SCI
DOI: 10.15672/hujms.470975
Keywords
maximal monotone operator; proximal point algorithm; Hadamard space; nonexpansive mapping; resolvent operator
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In this paper, we consider a proximal point algorithm for finding zeros of maximal monotone operators in complete CAT(0) spaces. First, a necessary and sufficient condition is presented for the zero set of the operator to be nonempty. Afterwards, we prove that, under suitable conditions, the proposed algorithm converges strongly to the metric projection of some point onto the zero set of the involving maximal monotone operator.
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