Some fixed point results via a minimax approach

In this paper, we investigate a finite dimensional case of Ricceri's question [given a real normed space E, a closed, convex, and unbounded set X E, and a function f : X X, find suitable conditions under which, for each y X, the function defined by x J(x, y) := xf (x)yf (x) has at most one global minimum in X] by providing several general and numerical examples of a such function f .We observe that other alternatives on the choice of the functional J defined above could lead to new fixed point theorems from Ricceri's minimax approach.