FIRMLY NONEXPANSIVE MAPPINGS IN CLASSES OF GEODESIC SPACES

被引：110
|
作者：
Ariza-Ruiz, David [1 ]
Leustean, Laurentiu [2 ]
Lopez-Acedo, Genaro [1 ]
机构：
[1] Univ Seville, Dept Anal Matemat, Fac Matemat, E-41080 Seville, Spain
[2] Romanian Acad, Simion Stoilow Inst Math, RO-014700 Bucharest, Romania
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2014年 / 366卷 / 08期
关键词：
Firmly nonexpansive mappings; geodesic spaces; uniform convexity; Picard iterates; asymptotic regularity; Delta-convergence; proof mining; effective bounds; minimization problems; PROXIMAL POINT ALGORITHM; MONOTONE VECTOR-FIELDS; ASYMPTOTIC-BEHAVIOR; ACCRETIVE-OPERATORS; NONLINEAR OPERATORS; CONVERGENCE; ITERATIONS; REGULARITY; THEOREMS; SETS;
D O I：
10.1090/S0002-9947-2014-05968-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Firmly nonexpansive mappings play an important role in metric fixed point theory and optimization due to their correspondence with maximal monotone operators. In this paper we do a thorough study of fixed point theory and the asymptotic behaviour of Picard iterates of these mappings in different classes of geodesic spaces, such as (uniformly convex) W-hyperbolic spaces, Busemann spaces and CAT(0) spaces. Furthermore, we apply methods of proof mining to obtain effective rates of asymptotic regularity for the Picard iterations.
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页码：4299 / 4322
页数：24
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