Some Convergence Theorems of Modified Proximal Point Algorithms for Nonexpansive Mappings in CAT(0) Spaces

Authors : Shengquan WENG, Dingping WU

Pages : 49-57

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Publication Date : 2018-08-31

Article Type : Research Paper

Abstract :In this paper, a new modified proximal point algorithm is proposed for finding a common element of the set of fixed points of a single-valued  nonexpansive mapping, and the set of fixed points of a multivalued nonexpansive mapping, and the set of minimizers of convex and lower semicontinuous  functions. We obtain convergence of the proposed algorithm to a common element of three sets in CATinsert ignore into journalissuearticles values(0); spaces.
Keywords : CAT 0, space, proximal point algorithm, fixed point, resolvent identity, functional analysis