Liu, Zeqing; Wang, Lili; Ume, Jeong Sheok; Kang, Shin Min Solvability and iterative algorithms for a system of generalized nonlinear mixed quasivariational inclusions with \((H_i,{\eta}_i)\)-monotone operators. (English) Zbl 1524.47077 J. Inequal. Appl. 2012, Paper No. 235, 13 p. (2012). Summary: In this paper, we introduce and discuss a new system of generalized nonlinear mixed quasivariational inclusions with \((H_i,{\eta}_i)\)-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 \((H_i,{\eta}_i)\)-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. MSC: 47J22 Variational and other types of inclusions 47H05 Monotone operators and generalizations 47H04 Set-valued operators 49J40 Variational inequalities Keywords:\((H_i,{\eta}_i)\)-monotone operators; resolvent operator technique; iterative algorithm; Mann perturbed iterative algorithm with mixed errors; set-valued mapping; convergence; system of generalised nonlinear mixed quasivariational inclusions; Hilbert space PDFBibTeX XMLCite \textit{Z. Liu} et al., J. Inequal. Appl. 2012, Paper No. 235, 13 p. (2012; Zbl 1524.47077) Full Text: DOI References: [1] doi:10.1016/S0893-9659(04)90073-0 · Zbl 1056.49008 · doi:10.1016/S0893-9659(04)90073-0 [2] doi:10.1016/S0096-3003(03)00275-3 · Zbl 1030.49008 · doi:10.1016/S0096-3003(03)00275-3 [3] doi:10.1016/j.camwa.2004.04.037 · Zbl 1068.49003 · doi:10.1016/j.camwa.2004.04.037 [4] doi:10.1016/j.camwa.2004.02.009 · Zbl 1059.49016 · doi:10.1016/j.camwa.2004.02.009 [5] doi:10.1016/S0096-3003(03)00192-9 · Zbl 1044.65057 · doi:10.1016/S0096-3003(03)00192-9 [6] doi:10.1002/mana.200310044 · Zbl 1032.47044 · doi:10.1002/mana.200310044 [7] doi:10.1023/A:1016079130417 · Zbl 1019.58006 · doi:10.1023/A:1016079130417 [8] doi:10.1016/j.jmaa.2006.04.015 · Zbl 1104.49012 · doi:10.1016/j.jmaa.2006.04.015 [9] doi:10.1006/jmaa.1994.1361 · Zbl 0820.49005 · doi:10.1006/jmaa.1994.1361 [10] doi:10.1016/j.camwa.2004.12.017 · Zbl 1081.49011 · doi:10.1016/j.camwa.2004.12.017 [11] doi:10.1006/jmaa.1995.1289 · Zbl 0872.47031 · doi:10.1006/jmaa.1995.1289 [12] doi:10.2140/pjm.1969.30.475 · Zbl 0187.45002 · doi:10.2140/pjm.1969.30.475 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.