Proximal point algorithms involving fixed points of nonexpansive mappings in CAT(0) spaces

In this paper, we introduce a new modified proximal point algorithm involving fixed point iterates of nonexpansive mappings in CAT ( 0 ) spaces and prove that the sequence generated by our iterative process converges to a minimizer of a convex function and a fixed point of mappings.

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Vydané v:Fixed point theory and applications (Hindawi Publishing Corporation) Ročník 2015; číslo 1
Hlavní autori: Cholamjiak, Prasit, Abdou, Afrah AN, Cho, Yeol Je
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 10.12.2015
Predmet:
Analysis
Applications of Mathematics
Differential Geometry
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Recent Progress in Fixed Point Theory and Applications
Topology
47H10
convex minimization problem
47H09
nonexpansive mapping
space
proximal point algorithm
resolvent identity
ISSN:1687-1812, 1687-1812
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Popis
Shrnutí:In this paper, we introduce a new modified proximal point algorithm involving fixed point iterates of nonexpansive mappings in CAT ( 0 ) spaces and prove that the sequence generated by our iterative process converges to a minimizer of a convex function and a fixed point of mappings.
ISSN:1687-1812
1687-1812
DOI:10.1186/s13663-015-0465-4