Solvability and iterative algorithms for a system of generalized nonlinear mixed quasivariational inclusions with (Hi,ηi)-monotone operators

被引：0
作者：
Zeqing Liu
Lili Wang
Jeong Sheok Ume
Shin Min Kang
机构：
[1] Liaoning Normal University,Department of Mathematics
[2] Changwon National University,Department of Mathematics
[3] Gyeongsang National University,Department of Mathematics and RINS
来源：
Journal of Inequalities and Applications | / 2012卷
关键词：
-monotone operators; resolvent operator technique; iterative algorithm; Mann perturbed iterative algorithm with mixed errors; set-valued mapping; convergence; system of generalized nonlinear mixed quasivariational inclusions; Hilbert space;
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摘要：
In this paper, we introduce and discuss a new system of generalized nonlinear mixed quasivariational inclusions with (Hi,ηi)-monotone operators in Hilbert spaces, which includes several systems of variational inequalities and variational inclusions as special cases. By employing the resolvent operator technique associated with (Hi,ηi)-monotone operators, we suggest two iterative algorithms for computing the approximate solutions of the system of generalized nonlinear mixed quasivariational inclusions. Under certain conditions, we obtain the existence of solutions for the system of generalized nonlinear mixed quasivariational inclusions and prove the convergence of the iterative sequences generated by the iterative algorithms. The results presented in this paper extend, improve and unify many known results in recent literature.
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