FIXED POINT THEOREM OF CONE EXPANSION AND COMPRESSION OF FUNCTIONAL TYPE Summary: FIXED POINT THEOREM OF CONE EXPANSION AND COMPRESSION OF FUNCTIONAL TYPE RICHARD I. AVERY AND DOUGLAS R. ANDERSON1 Abstract. The fixed point theorem of cone expansion and compression of norm type is generalized by replacing the norms with two functionals satisfying certain conditions to produce a fixed point theorem of cone expansion and compression of functional type. We conclude with an application verifying the existence of a positive solution to a discrete second-order conjugate boundary value problem. Dedicated to Allan Peterson on the occasion of his 60th birthday. 1. Preliminaries There are many fixed point theorems. See [7] for an introduction to the study and applications of fixed point theorems. In this paper we will generalize the fixed point theorem of cone expansion and compression of norm type. The generalization allows the user to choose two functionals that satisfy certain conditions which are used in place of the norm. In applications to boundary value problems the functionals will typically be the minimum or maximum of the function over a specific interval. Hence in boundary value problem applications the functionals usually do not satisfy the triangle inequality property of a norm. The flexibility of using functionals instead of norms allows the theorem to be used in a wider variety of situations. In particular, in applications to boundary value problems it allows for improved sufficiency conditions for the existence of a positive solution. Collections: Mathematics