Systems of Set-Valued Quasivariational Inclusion Problems

We propose four kinds of systems of set-valued quasivariational inclusion problems in product spaces, which include many known systems of equilibrium problems and systems of variational inequalities as well as inclusion problems. Sufficient conditions for the solution existence are established. When applied to special cases, these conditions improve many existing results in the literature. To ensure the generality of our problem setting and results, applications in fixed-point theory and quasioptimization problems are included. This work was partially supported by the Vietnam national program on basic research in natural sciences. A part of the work of the first author was completed during his stay at the Department Mathematics of Namur University and its hospitality is gratefully acknowledged. The authors are indebted to an anonymous referee for valuable remarks.