Electronic Journal of Differential Equations, Vol. 2010(2010), No. 53, pp. 1-11. Title: Two modifications of the Leggett-Williams fixed point theorem and their applications Author: Kyriakos G. Mavridis (Univ. of Ioannina, Greece) Abstract: This article presents two modifications of the Leggett-Williams fixed point theorem, and two applications of these results to a terminal and to a boundary value problem for ordinary differential equations. Submitted February 15, 2010. Published April 14, 2010. Math Subject Classifications: 47H10, 34B40, 34K10, 34B18. Key Words: Leggett-Williams fixed point theorem; positive solutions of boundary value problems; functional second order differential equations.