Fixed-Point Theorem And Generalized Variational Inclusion In H-space

In this paper, we study fixed-point theorems for two maps, minimax inequalities and the existence results for generalized nonlinear variational inclusions in H-space.In chapter one, we present some basic definitions, notions and facts that will be used later in this paper.In chapter two, we prove a new fixed-point theorem for two maps defined on H-space, only one of them satisfies a noncompactness condition. We also obtain a new intersection theorem by the fixed-point theorem in this chapter.In chapter three, we apply the intersection theorem to get some new minimax inequalities of Sion's type in H-space.In chapter four, we consider a more general form of generalized nonlinear variational inclusions and prove the existence of solutions for these variational inclusions in H-space.