ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS WITH RESPECT TO THE BREGMAN DISTANCE IN THE INTERMEDIATE SENSE

被引：2
作者：
Tomizawa, Yukino [1 ]
机构：
[1] Chuo Univ, Fac Sci & Engn, Dept Math, Bunkyo Ku, 1-13-27 Kasuga, Tokyo 1128551, Japan
来源：
FIXED POINT THEORY | 2017年 / 18卷 / 01期
关键词：
Bregman distance; Bregman projection; asymptotically quasi-nonexpansive in the intermediate sense; fixed point; Legendre function; totally convex function; STRONG-CONVERGENCE THEOREMS; FIXED-POINTS; TOTAL CONVEXITY; PROJECTIONS; WEAK; OPERATORS; SETS;
D O I：
10.24193/fpt-ro.2017.1.31
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The purpose of this paper is to introduce a new class of nonlinear mappings which is an extension of asymptotically quasi-nonexpansive mappings with respect to the Bregman distance 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.
引用
收藏
页码：391 / 405
页数：15
相关论文
共 38 条
  • [1] Alber Y. I., 1996, THEORY APPL NONLINEA, V178, P15
  • [2] [Anonymous], J INEQUAL APPL
  • [3] [Anonymous], INT J MATH ANAL
  • [4] [Anonymous], J FIXED POINT THEORY
  • [5] Barbu V, 2010, SPRINGER MONOGR MATH, P1, DOI 10.1007/978-1-4419-5542-5
  • [6] Chebyshev Sets, Klee Sets, and Chebyshev Centers with Respect to Bregman Distances: Recent Results and Open Problems
    Bauschke, Heinz H.
    Macklem, Mason S.
    Wang, Xianfu
    [J]. FIXED-POINT ALGORITHMS FOR INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2011, 49 : 1 - 21
  • [7] Bregman distances and Chebyshev sets
    Bauschke, Heinz H.
    Wang, Xianfu
    Ye, Jane
    Yuan, Xiaoming
    [J]. JOURNAL OF APPROXIMATION THEORY, 2009, 159 (01) : 3 - 25
  • [8] Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces
    Bauschke, HH
    Borwein, JM
    Combettes, PL
    [J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2001, 3 (04) : 615 - 647
  • [9] Borwein JM, 1999, NATO ADV SCI I C-MAT, V528, P61
  • [10] Bregman L. M., 1967, USSR COMP MATH MATH, V7, P200, DOI [10.1016/0041- 5553(67)90040-7, 10.1016/0041-5553(67)90040-7]
1234