求解实Banach空间中变分包含问题的松弛修正Tseng算法及其应用

IF 1.4 4区数学 Q1 MATHEMATICS

Carpathian Journal of Mathematics Pub Date : 2022-07-30 DOI:10.37193/cjm.2023.01.01

A. Abubakar, Kumam Poom, Kitkuan Duangkamon, Padcharoen Anantachai

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引用次数: 4

摘要

本文介绍并研究了两个单调算子的和的零点逼近的松弛和松弛惯性修正Tseng算法，这些算子的零点是某些非扩张型映射的不动点或J不动点并对J不动点的概念、凸极小化、图像恢复和信号恢复等问题进行了讨论。此外，还介绍了我们提出的方法在解决图像恢复和压缩传感问题中的一些有趣的数值实现。最后，将我们提出的方法的性能与文献中现有的一些方法进行了比较。“

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Relaxed modified Tseng algorithm for solving variational inclusion problems in real Banach spaces with applications

"In this paper, relaxed and relaxed inertial modified Tseng algorithms for approximating zeros of sum of two monotone operators whose zeros are fixed points or J-fixed points of some nonexpansive-type mappings are introduced and studied. Strong convergence theorems are proved in the setting of real Banach spaces that are uniformly smooth and 2-uniformly convex. Furthermore, applications of the theorems to the concept of J-fixed point, convex minimization, image restoration and signal recovery problems are also presented. In addition, some interesting numerical implementations of our proposed methods in solving image recovery and compressed sensing problems are presented. Finally, the performance of our proposed methods are compared with that of some existing methods in the literature."

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来源期刊

Carpathian Journal of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Carpathian Journal of Mathematics publishes high quality original research papers and survey articles in all areas of pure and applied mathematics. It will also occasionally publish, as special issues, proceedings of international conferences, generally (co)-organized by the Department of Mathematics and Computer Science, North University Center at Baia Mare. There is no fee for the published papers but the journal offers an Open Access Option to interested contributors.