Document Type : Research Paper
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Mathematics Faculty of Science Islamic Azad University Central Tehran Branch
Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran
The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions admitting only the existence of a mixed $\leq$-solution.