In this paper, we consider the implicit quasi-variational inequality without continuity assumptions of data mappings. Our approach here is completely different from the one based on KKM theorem in the literature. Interesting applications to generalized quasi-variational inequalities for both...

This paper deals with generalized vector quasi-equilibrium problems. Using a so-called nonlinear scalarization function and a fixed point theorem, existence theorems for two classes of generalized vector quasi-equilibrium problems are established. Copyright Springer-Verlag 2005

The aim of this paper is to solve the fixed point problems: <Equation ID="Equa"> <EquationSource Format="TEX">$$ v=\mathcal{O}v,\quad \hbox{with}\, \mathcal{O}v(x) \mathop{=}^{\rm def} \max (Lv(x), Bv(x) ), x \in \varepsilon, \quad (1)$$</EquationSource> </Equation> where <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\varepsilon$$</EquationSource> </InlineEquation> is a finite set, L is contractive and B is a nonexpansive operator and <Equation ID="Equb"> <EquationSource Format="TEX">$$...</equationsource></equation></equationsource></inlineequation></equationsource></equation>

In this paper, we establish a continuous selection theorem and use it to derive five equivalent results on the existence of fixed points, sectional points, maximal elements, intersection points and solutions of variational relations, all in topological settings without linear structures. Then,...