Generalized systems of variational inequalities and projection methods for inverse-strongly monotone mappings (Q659566)

Summary: We introduce an iterative sequence for finding a common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for three inverse-strongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we find solutions of a general system of variational inequalities and a zero of a maximal monotone operator in a real Hilbert space. As applications, at the end of the paper we utilize our results to study some convergence problem for strictly pseudocontractive mappings. Our results include previous results as special cases and extend and improve the results of \textit{L.-C. Ceng} et al. [Math. Methods Oper. Res. 67, No. 3, 375--390 (2008; Zbl 1147.49007)] and many others.