Dynamical and proximal approaches for approximating fixed points of quasi-nonexpansive mappings

被引：4

作者：

Khatibzadeh, Hadi ^{[1
]}

Piranfar, Mohsen Rahimi ^{[2
]}

Rooin, Jamal ^{[2
]}

机构：

[1] Univ Zanjan, Dept Math, POB 45195-313, Zanjan, Iran

[2] Inst Adv Studies Basic Sci, Dept Math, POB 45195-1159, Zanjan, Iran

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2018年 / 20卷 / 02期

关键词：

Quasi-nonexpansive mapping; fixed point; evolution equation; asymptotic behavior; proximal point algorithm; rate of convergence; CONTRACTION SEMIGROUPS; ASYMPTOTIC-BEHAVIOR; WEAK-CONVERGENCE; GRADIENT; OPERATORS; SEQUENCE; SYSTEMS; CONVEX;

D O I：

10.1007/s11784-018-0539-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we derive some weak and strong convergence results for a nonhomogeneous differential equation with a Lipschitz quasi-nonexpansive mapping. We also consider a discrete version that provides an iterative algorithm for approximating a fixed point of the mapping. We state some weak and strong convergence results related to this algorithm. Finally, we compare this algorithm with the classical algorithms for approximating fixed points of quasi-nonexpansive mappings, and show the advantage of the proposed algorithm via convergence rates.

引用

页数：14

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