Kazmi, K. R.; Alvi, Shakeel Ahmad Existence and iterative approximation of solutions of multi-valued generalized quasi-variational-like inequalities: an auxiliary principle approach. (English) Zbl 1188.49011 South East Asian J. Math. Math. Sci. 7, No. 2, 27-38 (2009). Summary: We consider an auxiliary problem for a generalized quasi-variational-like inequality problem involving multi-valued mappings in real Hilbert space and establish an existence and uniqueness result for this auxiliary problem. Using this result, we construct an algorithm for the generalized quasi-variational-like inequality problem. Further, we prove the existence of a solution of a generalized quasi-variational-like inequality problem and discuss convergence criteria of the algorithm. MSC: 49J40 Variational inequalities 47J20 Variational and other types of inequalities involving nonlinear operators (general) Keywords:multi-valued generalized quasi-variational-like in equality problem; auxiliary problem; strongly mixed monotone mapping; mixed; Lipschitz continuous mapping; coercive mapping PDFBibTeX XMLCite \textit{K. R. Kazmi} and \textit{S. A. Alvi}, South East Asian J. Math. Math. Sci. 7, No. 2, 27--38 (2009; Zbl 1188.49011)