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Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces

机译：通过多值耦合逼近集合之间的距离并应用于均匀凸的Banach空间

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摘要

In this paper, our aim is to ascertain the distance between two sets iteratively in two simultaneous ways with the help of a multivalued coupling define for this purpose. We define the best proximity points of such couplings that realize the distance between two sets. Our main theorem is deduced in metric spaces. As an application, we obtain the corresponding results in uniformly convex Banach spaces using the geometry of the space. We discuss two examples.

机译：在本文中，我们的目的是借助为此目的定义的多值耦合，以两种同时的方式迭代确定两个集合之间的距离。我们定义此类联轴器的最佳接近点，以实现两组之间的距离。我们的主要定理是在度量空间中推导的。作为应用程序，我们使用空间的几何在均匀凸Banach空间中获得了相应的结果。我们讨论两个例子。

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期刊名称 Springer Open Choice
作者
Binayak S. Choudhury; Pranati Maity; Nikhilesh Metiya; Mihai Postolache;
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作者单位

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年(卷),期 -1(2018),1
年度 -1
页码 130
总页数 15
原文格式 PDF
正文语种
中图分类外科学;
关键词
Metric spaces Coupling Best proximity pair Optimal approximate solution Uniformly convex Banach space;

机译：度量空间;耦合;最佳邻近对;最佳近似解;一致凸Banach空间;

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专利

1. Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces [J] . Binayak S. Choudhury, Pranati Maity, Nikhilesh Metiya, Journal of inequalities and applications . 2018,第1期

机译：通过多值耦合逼近集合之间的距离并应用于均匀凸的Banach空间
2. New iterative algorithm for two infinite families of multivalued quasi-nonexpansive mappings in uniformly convex banach spaces [J] . Zhang F., Zhang H., Zhang Y. Journal of applied mathematics . 2013,第Pta3期

机译：一致凸Banach空间中两个无限族的多值拟非扩张映射的新迭代算法
3. New Iterative Algorithm for Two Infinite Families of Multivalued Quasi-Nonexpansive Mappings in Uniformly Convex Banach Spaces [J] . FangZhang, HuanZhang, YulongZhang Journal of applied mathematics . 2013,第1期

机译：一致凸Banach空间中两个无限多值拟非扩张映象族的迭代算法
4. Mixed iterative scheme for equilibrium problems, variational inequalities, zero point problems and fixed point problems in 2-uniformly convex Banach spaces [C] . Duan Li-Ling, Fan Shu-Xin, Li Wei Proceedings of 2011 International Conference on Wavelet Analysis and Pattern Recognition . 2011

机译：2一致凸Banach空间中平衡问题，变分不等式，零点问题和不动点问题的混合迭代方案
5. On the density of the Henig efficient points of asymptotically compact sets in locally convex vector spaces. [D] . Newhall, J. F. 2010

机译：关于局部凸向量空间中渐近紧集的Henig有效点的密度。
6. Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications [O] . Yongchun Xu, Jinyu Guan, Yanxia Tang, -1

机译：非膨胀算子方程的多元系统及其在一致凸和一致光滑Banach空间中求解它们的迭代算法及其应用
7. Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces [O] . Binayak S. Choudhury, Pranati Maity, Nikhilesh Metiya, 2018

机译：用施加均匀耦合到均匀凸起的Banach空间近似距离近似距离
8. Convex closed set-valued operators in Banach spaces and their applications in control problems [R] . Vu Ngoc Phat, Jong Yeoul Park 1995

机译：Banach空间中的凸集闭集集值运算符及其在控制问题中的应用

Approximating distance between sets by multivalued coupling with application to uniformly convex Banach spaces

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