Qin, Xiaolong; Cho, Sun Young; Kang, Shin Min Some results on variational inequalities and generalized equilibrium problems with applications. (English) Zbl 1216.47099 Comput. Appl. Math. 29, No. 3, 393-421 (2010). The purpose of this paper is to introduce a general iterative method for finding a common element of the set of solutions of generalized equilibrium problems, the set of solutions of variational inequalities, and the set of common fixed points of a family of nonexpansive mappings in the framework of Hilbert spaces.The results presented in this paper improve and extend many known results. Reviewer: Hengyou Lan (Zigong) Cited in 1 ReviewCited in 4 Documents MSC: 47J25 Iterative procedures involving nonlinear operators 47J20 Variational and other types of inequalities involving nonlinear operators (general) 49J40 Variational inequalities 90C31 Sensitivity, stability, parametric optimization 47H05 Monotone operators and generalizations 47E05 General theory of ordinary differential operators 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics Keywords:sensitivity; stability; monotone operators; ordinary differential operators; generalised equilibrium problem; variational inequality; fixed point; nonexpansive mapping PDFBibTeX XMLCite \textit{X. Qin} et al., Comput. Appl. Math. 29, No. 3, 393--421 (2010; Zbl 1216.47099) Full Text: DOI