Kannan's fixed point approximation for solving split feasibility and variational inequality problems

被引：54
作者：
Berinde, Vasile [1 ,2 ]
Pacurar, Madalina [3 ]
机构：
[1] Tech Univ Cluj Napoca, North Univ Ctr Baia Mare, Dept Math & Comp Sci Tech, Victoriei 76, Baia Mare 430122, Romania
[2] Acad Romanian Scientists, Bucharest, Romania
[3] Babes Bolyai Univ Cluj Napoca, Fac Econ & Business Adm, Dept Econ & Business Adm German Language, T Mihali 58-60, Cluj Napoca 400591, Romania
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2021年 / 386卷
关键词：
Enriched Kannan mapping; Enriched Bianchini mapping; Fixed point; Krasnoselskij iteration; Split feasibility problem; Variational inequality problem; ENRICHED NONEXPANSIVE-MAPPINGS; BANACH-SPACES; THEOREMS;
D O I：
10.1016/j.cam.2020.113217
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this paper is to introduce a large class of mappings, called enriched Kannan mappings, that includes all Kannan mappings and some nonexpansive mappings. We study the set of fixed points and prove a convergence theorem for the Krasnoselskij iteration used to approximate fixed points of enriched Kannan mappings in Banach spaces. We further extend these mappings to the class of enriched Bianchini mappings. Examples to illustrate the effectiveness of our results are given. As applications of our main fixed point theorems, we present two Krasnoselskij projection type algorithms for solving split feasibility problems and variational inequality problems in the class of enriched Kannan mappings and enriched Bianchini mappings, respectively. (C) 2020 Elsevier B.V. All rights reserved.
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页数：9
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