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

#### Shengquan Weng [1] , Dingping Wu [2]

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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 CAT(0) spaces.

CAT(0) space, proximal point algorithm, fixed point, resolvent identity, functional analysis
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Primary Language en Articles Author: Shengquan Weng (Primary Author)Institution: Department of Applied Mathematics, Chengdu University of Information Technology, Chengdu, 610225, ChinaCountry: China Author: Dingping WuInstitution: Department of Applied Mathematics, Chengdu University of Information Technology, Chengdu, 610225, ChinaCountry: China
 Bibtex @research article { rna426161, journal = {Results in Nonlinear Analysis}, issn = {}, eissn = {2636-7556}, address = {Erdal KARAPINAR}, year = {2018}, volume = {1}, pages = {49 - 57}, doi = {}, title = {Some Convergence Theorems of Modified Proximal Point Algorithms for Nonexpansive Mappings in CAT(0) Spaces}, key = {cite}, author = {Weng, Shengquan and Wu, Dingping} } APA Weng, S , Wu, D . (2018). Some Convergence Theorems of Modified Proximal Point Algorithms for Nonexpansive Mappings in CAT(0) Spaces. Results in Nonlinear Analysis, 1 (2), 49-57. Retrieved from http://dergipark.org.tr/rna/issue/37067/426161 MLA Weng, S , Wu, D . "Some Convergence Theorems of Modified Proximal Point Algorithms for Nonexpansive Mappings in CAT(0) Spaces". Results in Nonlinear Analysis 1 (2018): 49-57 Chicago Weng, S , Wu, D . "Some Convergence Theorems of Modified Proximal Point Algorithms for Nonexpansive Mappings in CAT(0) Spaces". Results in Nonlinear Analysis 1 (2018): 49-57 RIS TY - JOUR T1 - Some Convergence Theorems of Modified Proximal Point Algorithms for Nonexpansive Mappings in CAT(0) Spaces AU - Shengquan Weng , Dingping Wu Y1 - 2018 PY - 2018 N1 - DO - T2 - Results in Nonlinear Analysis JF - Journal JO - JOR SP - 49 EP - 57 VL - 1 IS - 2 SN - -2636-7556 M3 - UR - Y2 - 2018 ER - EndNote %0 Results in Nonlinear Analysis Some Convergence Theorems of Modified Proximal Point Algorithms for Nonexpansive Mappings in CAT(0) Spaces %A Shengquan Weng , Dingping Wu %T Some Convergence Theorems of Modified Proximal Point Algorithms for Nonexpansive Mappings in CAT(0) Spaces %D 2018 %J Results in Nonlinear Analysis %P -2636-7556 %V 1 %N 2 %R %U ISNAD Weng, Shengquan , Wu, Dingping . "Some Convergence Theorems of Modified Proximal Point Algorithms for Nonexpansive Mappings in CAT(0) Spaces". Results in Nonlinear Analysis 1 / 2 (May 2018): 49-57.