共查询到20条相似文献,搜索用时 15 毫秒
1.
《Mathematical and Computer Modelling》1999,29(5):1-11
In this paper, we introduce and study a new class of variational inequalities, which is called the set-valued mixed quasi-variational inequality. The resolvent operator technique is used to establish the equivalence among generalized set-valued mixed quasi-variational inequalities, fixed-point problems and the set-valued implicit resolvent equations. This equivalence is used to study the existence of a solution of set-valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems. The results proved in this paper represent a significant refinement and improvement of the previously known results in this area. 相似文献
2.
In this paper, we introduce and study a new class of variational inequalities, which is called the generalized mixed variational inequality. Using essentially the resolvent operator concept, we establish the equivalence between the generalized mixed variational inequalities and the system of resolvent equations. This equivalence is used to suggest a number of new iterative algorithms for solving the variational inequalities. Several special cases are discussed which can be obtained from the main results of this paper. 相似文献
3.
广义非线性集值混合拟变分包含的扰动近似点算法 总被引:7,自引:0,他引:7
本文研究一类广义非线性集值混合拟变分包含,概括了尚明生等人引入与研究过的熟知的广义集值变分包含类成特例.运用预解算子的技巧,建立了广义非线性集值混合拟变分包含与不动点问题之间的等价性,其中,预解算子JρA(·,x)是具有常数1/(1+cρ)的Lipschitz连续算子.本文还建立了几个扰动迭代算法,并提供了由算法生成的逼近解的收敛判据,所得算法与结果改进与推广了尚明生等人的相应算法与结果. 相似文献
4.
5.
Banach空间中广义集值变分包含问题的迭代解 总被引:1,自引:0,他引:1
本文研究Banach空间中一类广义集值变分包含问题 ,建立了广义集值变分包含问题的迭代解的一些算法 ,并统一和推广了一些最新文献中的结果 . 相似文献
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7.
In this paper, we establish the equivalence between the generalized nonlinear mixed variational inequalities and the generalized resolvent equations. This equivalence is used to suggest and analyze a number of iterative algorithms for solving generalized variational inequalities. We also discuss the convergence analysis of the proposed algorithms. As special cases, we obtain various known results from our results. 相似文献
8.
9.
Salahuddin 《Journal of Mathematical Analysis and Applications》2004,298(1):146-156
In this paper, we develop the sensitivity analysis for generalized set-valued variational inclusions and generalized resolvent equations. We establish the equivalence between the parametric generalized set-valued variational inclusions and parametric generalized resolvent equations, by using the resolvent operator technique without assuming the differentiability of the given data. 相似文献
10.
Muhammad Aslam Noor 《Journal of Applied Mathematics and Computing》2000,7(1):101-113
In this paper, we introduce and study a new class of variational inclusions, called the set-valued quasi variational inclusions.
The resolvent operator technique is used to establish the equivalence between the set-valued quasi variational inclusions
and the fixed point problem. This equivalence is used to study the existence of a solution and to suggest a number of iterative
algorithms for solving the set-valued variational inclusions. We also study the convergence criteria of these algorithms. 相似文献
11.
《Applied Mathematics Letters》2004,17(1):43-48
In this paper, by using the concept of the resolvent operator, we study the behavior and sensitivity analysis of the solution set for a class of parametric generalized mixed variational inequalities with set-valued mappings. 相似文献
12.
In this paper we introduce and study a number of new classes of quasi variational inequalities. Using essentially the projection technique and its variant forms we prove that the generalized set-valued mixed quasivariational inequalities are equivalent to the fixed point problem and the Wiener-Hopf equations (normal maps). This equivalence enables us to suggest a number of iterative algorithms for solving the generalized variational inequalities. As a special case of the generalized set-valued mixed quasi variational inequalities, we obtain a class of quasi variational inequalities studied by Siddiqi, Husain and Kazmi [35], but there are several inaccuracies in their formulation of the problem, the statement and the proofs of their results. We have removed these inaccuracies. The correct formulation of their results can be obtained as special cases from our main results. 相似文献
13.
Narin Petrot 《Journal of Applied Mathematics and Computing》2010,32(2):393-404
The purpose of this paper is to suggest and analyze a number of iterative algorithms for solving the generalized set-valued variational inequalities in the sense of Noor in Hilbert spaces. Moreover, we show some relationships between the generalized set-valued variational inequality problem in the sense of Noor and the generalized set-valued Wiener-Hopf equations involving continuous operator. Consequently, by using the equivalence, we also establish some methods for finding the solutions of generalized set-valued Wiener-Hopf equations involving continuous operator. Our results can be viewed as a refinement and improvement of the previously known results for variational inequality theory. 相似文献
14.
In this paper, we introduce and consider a new class of mixed variational inequalities, which is called the general mixed
variational inequality. Using the resolvent operator technique, we establish the equivalence between the general mixed variational
inequalities and the fixed-point problems as well as resolvent equations. We use this alternative equivalent formulation to
suggest and analyze some iterative methods for solving the general mixed variational inequalities. We study the convergence
criteria of the suggested iterative methods under suitable conditions. Using the resolvent operator technique, we also consider
the resolvent dynamical systems associated with the general mixed variational inequalities. We show that the trajectory of
the dynamical system converges globally exponentially to the unique solution of the general mixed variational inequalities.
Our methods of proofs are very simple as compared with others’ techniques. Results proved in this paper may be viewed as a
refinement and important generalizations of the previous known results. 相似文献
15.
M. A. Noor 《分析论及其应用》1996,12(3):18-28
In this paper, we introduce and study a new class of quasi variational inequalities. Using essentially the projection technique
and its variant forms, we establish the equivalence between generalized nonlinear quasi variational inequalities and the fixed
point problems. This equivalence is then used to suggest and analyze a number of new iterative algorithms. These new results
include the corresponding known results for generalized quasi variational inequalities as special cases. 相似文献
16.
Some new classes of extended general nonconvex set-valued variational inequalities and the extended general Wiener-Hopf inclusions are introduced. By the projection technique, equivalence between the extended general nonconvex set-valued variational inequalities and the fixed point problems as well as the extended general nonconvex Wiener-Hopf inclusions is proved. Then by using this equivalent formulation, we discuss the existence of solutions of the extended general nonconvex set-valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of the extended general nonconvex set-valued variational inequalities. We also verify that the approximate solutions obtained by our algorithms converge to the solutions of the extended general nonconvex set-valued variational inequalities. The results presented in this paper extend and improve some known results from the literature. 相似文献
17.
In this paper, we introduce and study a new class of extended general nonlinear mixed variational inequalities and a new class of extended general resolvent equations and establish the equivalence between the extended general nonlinear mixed variational inequalities and implicit fixed point problems as well as the extended general resolvent equations. Then by using this equivalent formulation, we discuss the existence and uniqueness of solution of the problem of extended general nonlinear mixed variational inequalities. Applying the aforesaid equivalent alternative formulation and a nearly uniformly Lipschitzian mapping S, we construct some new resolvent iterative algorithms for finding an element of set of the fixed points of nearly uniformly Lipschitzian mapping S which is the unique solution of the problem of extended general nonlinear mixed variational inequalities. We study convergence analysis of the suggested iterative schemes under some suitable conditions. We also suggest and analyze a class of extended general resolvent dynamical systems associated with the extended general nonlinear mixed variational inequalities and show that the trajectory of the solution of the extended general resolvent dynamical system converges globally exponentially to the unique solution of the extended general nonlinear mixed variational inequalities. The results presented in this paper extend and improve some known results in the literature. 相似文献
18.
Muhammad Aslam Noor 《Optimization Letters》2009,3(3):437-451
In this paper, we introduce and consider a new system of general mixed variational inequalities involving three different
operators. Using the resolvent operator technique, we establish the equivalence between the general mixed variational inequalities
and the fixed point problems. We use this equivalent formulation to suggest and analyze some new explicit iterative methods
for this system of general mixed variational inequalities. We also study the convergence analysis of the new iterative method
under certain mild conditions. Since this new system includes the system of mixed variational inequalities involving two operators,
variational inequalities and related optimization problems as special cases, results obtained in this paper continue to hold
for these problems. Our results can be viewed as a refinement and improvement of the previously known results for variational
inequalities. 相似文献
19.
Muhammad Aslam Noor 《Journal of Applied Mathematics and Computing》1997,4(2):347-358
In this paper, we establish the equivalence between the general resolvent equations and variational inequalities. This equivalence is used to suggest and analyze a number of iterative algorithms for solving variational inclusions. We also study the convergence criteria of the iterative algorithms. Our results include several previously known results as special cases. 相似文献