An iterative method for solving minimization, variational inequality and fixed point problems in reflexive Banach spaces

被引：32
|
作者：
Jolaoso, Lateef Olakunle [1 ]
Ogbuisi, Ferdinard Udochukwu [1 ,2 ]
Mewomo, Oluwatosin Temitope [1 ]
机构：
[1] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, Durban, South Africa
[2] DST NRF Ctr Excellence Math & Stat Sci CoE MaSS, Johannesburg, South Africa
来源：
ADVANCES IN PURE AND APPLIED MATHEMATICS | 2018年 / 9卷 / 03期
基金：
新加坡国家研究基金会;
关键词：
Bregman distance; strong convergence; convex minimization problem; Legendre functions; Frechet differentiable functions; Gateaux differentiable function; resolvent; variational inequality; reflexive Banach space; Bregman projection;
D O I：
10.1515/apam-2017-0037
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we propose an iterative algorithm for approximating a common fixed point of an infinite family of quasi-Bregman nonexpansive mappings which is also a solution to finite systems of convex minimization problems and variational inequality problems in real reflexive Banach spaces. We obtain a strong convergence result and give applications of our result to finding zeroes of an infinite family of Bregman inverse strongly monotone operators and a finite system of equilibrium problems in real reflexive Banach spaces. Our result extends many recent corresponding results in literature.
引用
收藏
页码：167 / 184
页数：18
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