### Some fixed point theorems for multifunctions with applications in game theory

IntroductionThe main result of this paper is concerned with the conditions which guarantee that a multifunction $f:C\to {2}^{X}$ defined on an arbitrary subset C of a topological vector space X admits a point x of C such that x∈f(x).First, we give some definitions and propositions which are associated with semicontinuous multifunctions (Part 1).Next, in Part 2, we present a global convergence criterion on variable dimension algorithms for finding an approximate solution of the equation x∈f(x), and then we consider...