Weak convergence of infinite products of operators in Hadamard spaces

被引：48
作者：
Reich S. [1 ]
Salinas Z. [1 ]
机构：
[1] Department of Mathematics, The Technion-Israel Institute of Technology, Haifa
来源：
Rendiconti del Circolo Matematico di Palermo (1952 -) | 2016年 / 65卷 / 1期
基金：
以色列科学基金会;
关键词：
CAT(0)  space; Convex combination; Exact orbit; Firmly nonexpansive operator; Hadamard space; Inexact orbit; Infinite product; Nearest point projection; Strongly nonexpansive operator; Weak convergence;
D O I：
10.1007/s12215-015-0218-6
中图分类号：
学科分类号：
摘要：
We first prove the weak convergence of iterates of both products and convex combinations of strongly nonexpansive operators in complete CAT(0) spaces. Then we establish the weak convergence of infinite products of possibly discontinuous approximations to such operators. Our main focus is on nearest point projections. © 2015, Springer-Verlag Italia.
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页码：55 / 71
页数：16
相关论文
共 23 条
[1]  
Ariza-Ruiz D., Leustean L., Lopez-Acedo G., Firmly nonexpansive mappings in classes of geodesic spaces, Trans. Am. Math. Soc., 366, pp. 4299-4322, (2014)
[2]  
Bacak M., Convex analysis and optimization in hadamard spaces, (2014)
[3]  
Bacak M., Searston I., Sims B., Alternating projections in CAT(0) spaces, J. Math. Anal. Appl., 385, pp. 599-607, (2012)
[4]  
Baillon J.-B., Bruck R.E., Reich S., On the asymptotic behavior of nonexpansive mappings and semigroups in Banach spaces, Houston J. Math., 4, pp. 1-9, (1978)
[5]  
Bauschke H.H., Matouskova E., Reich S., Projection and proximal point methods: convergence results and counterexamples, Nonlinear Anal., 56, pp. 715-738, (2004)
[6]  
Bridson M.R., Haefliger A., Metric spaces of non-positive curvature, (1999)
[7]  
Bruck R.E., Reich S., Nonexpansive projections and resolvents of accretive operators in Banach spaces, Houston J. Math., 3, pp. 459-470, (1977)
[8]  
Butnariu D., Reich S., Zaslavski A.J., Convergence to fixed points of inexact orbits of Bregman-monotone and of nonexpansive operators in Banach spaces, Fixed Point Theory and Applications, (2006)
[9]  
Conway J.B., Functions of one complex variable, (1978)
[10]  
Dhompongsa S., Kirk W.A., Sims B., Fixed points of uniformly lipschitzian mappings, Nonlinear Anal., 65, pp. 762-772, (2006)
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