Quasi-intersection problems and fixed point theorems concerning separately scalar weakly I.s.c and u.s.c mappings

Abstract

In this paper, we first prove a new result on quasi-variational inequality problems; then, we use it to show the existence of solutions to quasi-intersection problems. In particular, we establish several results on the existence of solutions to generalized quasi-equilibrium problems and fixed point problems concerning separately scalar weakly lower and upper semi-continuous mappings. The results in this paper generalize some well known existence theorems from the literature.