Common coupled fixed point results for operators without mixed monotone type properties and application to nonlinear integral equations

Abstract We establish some new common coupled fixed point theorems for a pair of operators not assumed to satisfy mixed monotone type properties in the ordered Banach space setting. For that purpose, the notions of weakly inflationary and weakly deflationary operators are introduced in the two-dimensional setting, and existence and uniqueness common coupled fixed point theorems for such operators are established under certain condensing and contractive conditions involving the two-dimensional setting. As an application, we study the existence and uniqueness of nonnegative solutions for nonlinear integral equations.