单调映射和的零逼近及其在变分不等式和图像恢复问题中的应用

Q3 Mathematics Nonlinear Functional Analysis and Applications Pub Date : 2021-05-23 DOI:10.22771/NFAA.2021.26.02.12

A. Adamu, Jitsupa Deepho, A. Ibrahim, A. Abubakar

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引用次数: 9

摘要

本文介绍并研究了一类解为非线性映射不动点的单调包含问题的一种惯性halpern型正向后迭代逼近算法。在实数Hilbert空间中建立了强收敛定理。此外，我们的定理应用于变分不等式问题、凸最小化问题和图像恢复问题。最后，给出了数值实例来支持主要定理及其应用。

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APPROXIMATION OF ZEROS OF SUM OF MONOTONE MAPPINGS WITH APPLICATIONS TO VARIATIONAL INEQUALITY AND IMAGE RESTORATION PROBLEMS

In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.

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来源期刊

Nonlinear Functional Analysis and Applications Mathematics-Analysis

CiteScore

1.90

自引率

0.00%

发文量

期刊介绍： The international mathematical journal NFAA will publish carefully selected original research papers on nonlinear functional analysis and applications, that is, ordinary differential equations, all kinds of partial differential equations, functional differential equations, integrodifferential equations, control theory, approximation theory, optimal control, optimization theory, numerical analysis, variational inequality, asymptotic behavior, fixed point theory, dynamic systems and complementarity problems. Papers for publication will be communicated and recommended by the members of the Editorial Board.