Coupled fixed points of generalized Kanann contraction and its applications

Abstract

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 <span>Kanann</span> type <span>contractivity</span> 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 <span>$leq$</span>-solution.