Proximal point algorithms involving fixed point iteration for nonexpansive mappings in CAT(κ) spaces

被引：0

作者：

Pakkaranang, Nuttapol ^{[1
]}

Kumam, Poom ^{[1
,2
]}

Cholamjiak, Prasit ^{[3
]}

Suparatulatorn, Raweerote ^{[4
]}

Chaipunya, Parin ^{[1
]}

机构：

[1] KMUTT, Fac Sci, Kmuttfixed Point Res Lab, Dept Math, Room SCL 802 Fixed Point Lab,Sci Lab Bldg, Bangkok 10140, Thailand

[2] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

[3] Univ Phayao, Sch Sci, Phayao 56000, Thailand

[4] Chiang Mai Univ, Fac Sci, Dept Math, Chiangmai 50200, Thailand

来源：

CARPATHIAN JOURNAL OF MATHEMATICS | 2018年 / 34卷 / 02期

关键词：

Proximal point algorithm; Mann iteration; Resolvent; Nonexpansive mappings; CAT(kappa) spaces; COMPLETE GEODESIC SPACE; CONVEX-FUNCTIONS; CONVERGENCE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a new modified proximal point algorithm involving fixed point iteration for nonexpansive mappings in CAT(1) spaces. Under some mild conditions, we prove that the sequence generated by our iterative algorithm Delta-converges to a common solution between certain convex optimization and fixed point problems.

引用

页码：229 / 237

页数：9

共 33 条

[1] [Anonymous], 1999, METRIC SPACES NONPOS
[2] [Anonymous], 1986, CONVEXITY OPTIMIZATI
[3] FIRMLY NONEXPANSIVE MAPPINGS IN CLASSES OF GEODESIC SPACES
Ariza-Ruiz, David
Leustean, Laurentiu
Lopez-Acedo, Genaro
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 366 (08) : 4299 - 4322
[4] COMPUTING MEDIANS AND MEANS IN HADAMARD SPACES
Bacak, Miroslav
[J]. SIAM JOURNAL ON OPTIMIZATION, 2014, 24 (03) : 1542 - 1566
[5] The proximal point algorithm in metric spaces
Bacak, Miroslav
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2013, 194 (02) : 689 - 701
[6] On the proximal point method in Hadamard spaces
Chaipunya, Parin
Kumam, Poom
[J]. OPTIMIZATION, 2017, 66 (10) : 1647 - 1665
[7] Cholamjiak P, 2015, J NONLINEAR CONVEX A, V16, P109
[8] CAT(k)-spaces, weak convergence and fixed points
Espinola, Rafa
Fernandez-Leon, Aurora
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 353 (01) : 410 - 427
[9] Proximal point algorithm on Riemannian manifolds
Ferreira, OP
Oliveira, PR
[J]. OPTIMIZATION, 2002, 51 (02) : 257 - 270
[10] Mann's algorithm for nonexpansive mappings in CAT(κ) spaces
He, J. S.
Fang, D. H.
Lopez, G.
Li, C.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (02) : 445 - 452

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