scholarly journals Iterative Algorithms for New General Systems of Set-Valued Variational Inclusions Involving(A,η)-Maximal Relaxed Monotone Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ting-jian Xiong ◽  
Heng-you Lan
Keyword(s):  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
General System ◽  
Monotone Operators ◽  
Inclusion Problem ◽  
Operator Technique ◽  
Variational Inclusions ◽  
Variational Inclusion Problem ◽  
General Systems ◽  
Resolvent Operator Technique

We introduce and study a class of new general systems of set-valued variational inclusions involving(A,η)-maximal relaxed monotone operators in Hilbert spaces. By using the general resolvent operator technique associated with(A,η)-maximal relaxed monotone operators, we construct some new iterative algorithms for finding approximation solutions to the general system of set-valued variational inclusion problem and prove the convergence of this algorithm. Our results improve and extend some known results.

scholarly journals Stable Perturbed Iterative Algorithms for Solving New General Systems of Nonlinear Generalized Variational Inclusion in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Ting-jian Xiong ◽  
Heng-you Lan
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Iterative Algorithms ◽  
General System ◽  
Variational Inclusion ◽  
Operator Technique ◽  
Accretive Mappings ◽  
General Systems ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator

We introduce and study a new general system of nonlinear variational inclusions involving generalizedm-accretive mappings in Banach space. By using the resolvent operator technique associated with generalizedm-accretive mappings due to Huang and Fang, we prove the existence theorem of the solution for this variational inclusion system in uniformly smooth Banach space, and discuss convergence and stability of a class of new perturbed iterative algorithms for solving the inclusion system in Banach spaces. Our results presented in this paper may be viewed as an refinement and improvement of the previously known results.

scholarly journals Approximation solvability for a system of implicit nonlinear variational inclusions with Η-monotone operators

2018 ◽  
Vol 51 (1) ◽  
pp. 241-254
Author(s):  
Jong Kyu Kim ◽  
Muhammad Iqbal Bhat
Keyword(s):  
Iterative Algorithm ◽  
Resolvent Operator ◽  
Monotone Operators ◽  
Inner Product ◽  
Operator Technique ◽  
Variational Inclusions ◽  
Inclusion Problems ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator ◽  
New System

AbstractIn this paper, we introduce and study a new system of variational inclusions which is called a system of nonlinear implicit variational inclusion problems with A-monotone and H-monotone operators in semi-inner product spaces. We define the resolvent operator associated with A-monotone and H-monotone operators and prove its Lipschitz continuity. Using resolvent operator technique, we prove the existence and uniqueness of solution for this new system of variational inclusions. Moreover, we suggest an iterative algorithm for approximating the solution of this system and discuss the convergence analysis of the sequences generated by the iterative algorithm under some suitable conditions.

scholarly journals Completely generalized multivalued nonlinear quasi-variational inclusions

2002 ◽  
Vol 30 (10) ◽  
pp. 593-604 ◽  
Author(s):  
Zeqing Liu ◽  
Lokenath Debnath ◽  
Shin Min Kang ◽  
Jeong Sheok Ume
Keyword(s):  
Existence Theorems ◽  
Maximal Monotone ◽  
Iterative Algorithms ◽  
Monotone Mappings ◽  
Operator Technique ◽  
Variational Inclusions ◽  
New Class ◽  
Convergence Results ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator

We introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-variational inclusions. We establish both four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz, and generalized pseudocontractive mappings, and obtain a few convergence results of iterative sequences generated by the algorithms. The results presented in this paper extend, improve, and unify a lot of results due to Adly, Huang, Jou-Yao, Kazmi, Noor, Noor-Al-Said, Noor-Noor, Noor-Noor-Rassias, Shim-Kang-Huang-Cho, Siddiqi-Ansari, Verma, Yao, and Zhang.

scholarly journals A new system of variational inclusions with (H, η)-monotone operators

2006 ◽  
Vol 74 (2) ◽  
pp. 301-319 ◽  
Author(s):  
Jianwen Peng ◽  
Jianrong Huang
Keyword(s):  
Hilbert Spaces ◽  
Resolvent Operator ◽  
Iterative Algorithms ◽  
Operator Method ◽  
Monotone Operators ◽  
Variational Inclusions ◽  
Uniqueness Of Solutions ◽  
Special Cases ◽  
The Resolvent Operator ◽  
New System

In this paper, We introduce and study a new system of variational inclusions involving(H, η)-monotone operators in Hilbert spaces. By using the resolvent operator method associated with (H, η)-monotone operators, we prove the existence and uniqueness of solutions and the convergence of some new three-step iterative algorithms for this system of variational inclusions and its special cases. The results in this paper extends and improves some results in the literature.

scholarly journals Multi-Step Inertial Hybrid and Shrinking Tseng’s Algorithm with Meir–Keeler Contractions for Variational Inclusion Problems

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1548
Author(s):  
Yuanheng Wang ◽  
Mingyue Yuan ◽  
Bingnan Jiang
Keyword(s):  
Projection Method ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Inertial Method ◽  
Inclusion Problems ◽  
Variational Inclusion Problem ◽  
Convex Minimization Problems ◽  
Tseng’S Method

In our paper, we propose two new iterative algorithms with Meir–Keeler contractions that are based on Tseng’s method, the multi-step inertial method, the hybrid projection method, and the shrinking projection method to solve a monotone variational inclusion problem in Hilbert spaces. The strong convergence of the proposed iterative algorithms is proven. Using our results, we can solve convex minimization problems.

scholarly journals Generalized System for Relaxed Cocoercive Mixed Variational Inequalities and Iterative Algorithms in Hilbert Spaces

2012 ◽  
Vol 20 (3) ◽  
pp. 131-139
Author(s):  
Shuyi Zhang ◽  
Xinqi Guo ◽  
Dan Luan
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Resolvent Operator ◽  
Iterative Algorithms ◽  
Operator Technique ◽  
Mixed Variational Inequality ◽  
Generalized System ◽  
Resolvent Operator Technique ◽  
Mixed Variational Inequalities ◽  
The Resolvent Operator

Abstract The approximate solvability of a generalized system for relaxed co- coercive mixed variational inequality is studied by using the resolvent operator technique. The results presented in this paper extend and improve the main results of Chang et al.[1], He and Gu [2] and Verma [3, 4].

scholarly journals The zeros of monotone operators for the variational inclusion problem in Hilbert spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Pattanapong Tianchai
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Monotone Operators ◽  
Fixed Point Problem ◽  
Variational Inclusion ◽  
Feasibility Problem ◽  
Strong Convergence Theorem ◽  
Inclusion Problem ◽  
Point Problem ◽  
Variational Inclusion Problem

AbstractIn this paper, we introduce a regularization method for solving the variational inclusion problem of the sum of two monotone operators in real Hilbert spaces. We suggest and analyze this method under some mild appropriate conditions imposed on the parameters, which allow us to obtain a short proof of another strong convergence theorem for this problem. We also apply our main result to the fixed point problem of the nonexpansive variational inequality problem, the common fixed point problem of nonexpansive strict pseudocontractions, the convex minimization problem, and the split feasibility problem. Finally, we provide numerical experiments to illustrate the convergence behavior and to show the effectiveness of the sequences constructed by the inertial technique.

scholarly journals On a System of Nonlinear Variational Inclusions withHh,η-Monotone Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Zeqing Liu ◽  
Jeong Sheok Ume ◽  
Shin Min Kang
Keyword(s):  
Hilbert Spaces ◽  
Monotone Operators ◽  
Variational Inclusions ◽  
Iterative Approximation

This paper is concerned mainly with the existence and iterative approximation of solutions for a system of nonlinear variational inclusions involving the stronglyHh,η-monotone operators in Hilbert spaces. The results presented in this paper extend, improve, and unify many known results in the literature.

Sign in / Sign up

Export Citation Format

Share Document