A strong convergence theorem for Bregman asymptotically quasi-nonexpansive mappings in the intermediate sense

被引：0

作者：

Yukino Tomizawa

机构：

[1] Chuo University,Department of Mathematics, Graduate School of Science and Engineering

[2] Kaohsiung Medical University,Center for Fundamental Science

来源：

Fixed Point Theory and Applications | / 2014卷

关键词：

asymptotically quasi-nonexpansive in the intermediate sense; Bregman distance; Bregman projection; Legendre function; totally convex function;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

The purpose of this paper is to introduce a new class of Bregman asymptotically quasi-nonexpansive mappings in the intermediate sense. A strong convergence theorem of the shrinking projection method with the modified Mann iteration is established to find fixed points of the mappings in reflexive Banach spaces. This theorem generalizes some known results in the current literature.

引用

共 50 条

[21] Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings
Sun, ZH
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 286 (01) : 351 - 358
[22] An ergodic theorem for asymptotically nonexpansive mappings in the intermediate sense
Oka, H
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (06) : 1693 - 1703
[23] Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications
Fukhar-ud-din, Hafiz
Khan, Safeer Hussain
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 328 (02) : 821 - 829
[24] On Asymptotically Quasi-φ-Nonexpansive Mappings in the Intermediate Sense
Qin, Xiaolong
Wang, Lin
ABSTRACT AND APPLIED ANALYSIS, 2012,
[25] Strong convergence for three classes of uniformly equi-continuous and asymptotically quasi-nonexpansive mappings
Qin, Xiaolong
Su, Yongfu
Shang, Meijuan
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2008, 45 (01) : 29 - 40
[26] Weak and Strong Convergence Theorems for Finite Families of Asymptotically Quasi-Nonexpansive Mappings in Banach Spaces
Deng, Lei
Xiao, Juan
ABSTRACT AND APPLIED ANALYSIS, 2014,
[27] On the strong convergence of a modified S-iteration process for asymptotically quasi-nonexpansive mappings in a space
Sahin, Aynur
Basarir, Metin
FIXED POINT THEORY AND APPLICATIONS, 2013,
[28] Convergence theorems for equilibrium problem and asymptotically quasi-ϕ-nonexpansive mappings in the intermediate sense
Jae Ug Jeong
Fixed Point Theory and Applications, 2014
[29] Weak and Strong Convergence of an Implicit Iteration Process for a Finite Family of Asymptotically Quasi-Nonexpansive Mappings
Thianwan, S.
THAI JOURNAL OF MATHEMATICS, 2010, 8 (04): : 105 - 119
[30] Convergence theorems for equilibrium problem and asymptotically quasi-φ-nonexpansive mappings in the intermediate sense
Jeong, Jae Ug
FIXED POINT THEORY AND APPLICATIONS, 2014,

← 1 2 3 4 5 →