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Kannan’s fixed point approximation for solving split feasibility and variational inequality problems
Journal of Computational and Applied Mathematics ( IF 2.4 ) Pub Date : 2020-10-21 , DOI: 10.1016/j.cam.2020.113217
Vasile Berinde , Mădălina Păcurar

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.



中文翻译:

Kannan的不动点逼近法,用于解决分裂可行性和变分不等式问题

本文的目的是介绍一大类映射,称为丰富的Kannan映射,其中包括所有Kannan映射和一些非扩展映射。我们研究了不动点集,并证明了Krasnoselskij迭代的收敛定理,该迭代定理用于近似Banach空间中丰富的Kannan映射的不动点。我们进一步将这些映射扩展到丰富的Bianchini映射的类。举例说明了我们的结果的有效性。作为主要定点定理的应用,我们提出了两种Krasnoselskij投影类型算法,分别用于解决富集的Kannan映射和富集的Bianchini映射中的分裂可行性问题和变分不等式问题。

更新日期:2020-11-02
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