CONVERGENCE OF MANN'S ALTERNATING PROJECTIONS IN CAT(κ) SPACES

被引：1

作者：

Choi, Byoung Jin ^{[1
]}

机构：

[1] Chungbuk Natl Univ, Inst Ind & Appl Math, Dept Math, Cheongju 28644, South Korea

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2018年 / 98卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

convex feasibility problem; CAT(kappa) space; Delta-convergence; Mann's alternating projection method; NONEXPANSIVE-MAPPINGS; WEAK-CONVERGENCE; CAT(0) SPACES; FIXED-POINTS; THEOREMS; ALGORITHMS;

D O I：

10.1017/S0004972718000230

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the convex feasibility problem in CAT(kappa) spaces using Mann's iterative projection method. To do this, we extend Mann's projection method in normed spaces to CAT(kappa) spaces with kappa >= 0, and then we prove the Delta-convergence of the method. Furthermore, under certain regularity or compactness conditions on the convex closed sets, we prove the strong convergence of Mann's alternating projection sequence in CAT(kappa) spaces with kappa >= 0.

引用

页码：134 / 143

页数：10

共 19 条

[1] The Asymptotic Behavior of the Composition of Firmly Nonexpansive Mappings [J].