A new explicit iteration method for a class of variational inequalities

Buong, Nguyen; Ha, Nguyen Song; Thủy, Nguyễn Thị Thu

doi:10.1007/s11075-015-0056-9

Cited by 17 publications

(3 citation statements)

References 31 publications

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“…Proposition 2.1 [see, [12,13]] Let H and F be as in Lemma 2.1 and let T be a nonexpansive operator on H such that Fix(T ) = ∅. Then, for any bounded sequence {x k } ⊂ H such that…”

Section: Preliminariesmentioning

confidence: 99%

A Method of Approximation for a Zero of Maximal Monotone Operator in Hilbert Space

Hoài¹,

Hoa²,

Thắng³

2020

JST

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Trong bài báo này chúng tôi đưa ra một phương pháp lặp hiện mới giải bài toán bất đẳng thức biến phân trên tập không điểm của toán tử đơn điệu cực đại trong không gian Hilbert. Bằng việc sử dụng hai toán tử giải của một toán tử đơn điệu tại mỗi bước lặp, chúng tôi chứng minh sự hội tụ mạnh của phương pháp dưới điều kiện suy rộng đặt lên tham số.

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“…Proposition 2.1 [see, [12,13]] Let H and F be as in Lemma 2.1 and let T be a nonexpansive operator on H such that Fix(T ) = ∅. Then, for any bounded sequence {x k } ⊂ H such that…”

Section: Preliminariesmentioning

confidence: 99%

A Method of Approximation for a Zero of Maximal Monotone Operator in Hilbert Space

Hoài¹,

Hoa²,

Thắng³

2020

JST

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“…After that number of problems have been solved using S-iterative method and its modified version, see [2,3,16,22]. In recent past, Parallel iterative methods have been using by number of researchers with numerous applications, see, for example, [5,6,8,11,17,31]. Following these ongoing research techniques, Sahu [20] studied the altering points problem of nonlinear mappings and presented the convergence analysis of the following parallel S-iterative method.…”

Section: Introductionmentioning

confidence: 99%

Approximation of Iterative Methods for Altering Points Problem With Applications

Khan

Akram

Dilshad

2023

Mathematical Modelling and Analysis

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In this paper, we consider and investigate an altering points problem involving generalized accretive mappings over closed convex subsets of a real uniformly smooth Banach space. Parallel Mann and parallel S-iterative methods are suggested to analyze the approximate solution of altering points problem. Consequently, some systems of generalized variational inclusions and generalized variational inequalities are also explored using the conceptual framework of altering points. Convergence of suggested iterative methods are verified by an illustrative numerical example.

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“…Without this weak continuity, recently, in and , the author and Phuong suggested several implicit iterative and regularization methods when C is the set of common fixed points for an infinite family of nonexpansive mappings on E . Explicit iterative methods for the class of variational inequalities were considered in and .…”

Section: Introductionmentioning

confidence: 99%

Steepest‐descent proximal point algorithms for a class of variational inequalities in Banach spaces

Buong

2018

Mathematische Nachrichten

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In this paper, we present a new approach to the problem of finding a common zero for a system of m‐accretive mappings in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm. We propose an implicit iteration method and two explicit ones, based on compositions of resolvents with the steepest‐descent method. We show that our results contain some iterative methods in literature as special cases. An extension of the Xu's regularization method for the proximal point algorithm from Hilbert spaces onto Banach ones under simple conditions of convergence and a new variant for the method of alternating resolvents are obtained. Numerical experiments are given to affirm efficiency of the methods.

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A new explicit iteration method for a class of variational inequalities

Cited by 17 publications

References 31 publications

A Method of Approximation for a Zero of Maximal Monotone Operator in Hilbert Space

A Method of Approximation for a Zero of Maximal Monotone Operator in Hilbert Space

Approximation of Iterative Methods for Altering Points Problem With Applications

Steepest‐descent proximal point algorithms for a class of variational inequalities in Banach spaces

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