It is well known that a concave operator is important for studying positive solutions of nonlinear differential and integral equations. In this paper, we study a class of mixed monotone operators with convexity, also the properties of monotone iterative technique in ordered Banca spaces, some new existence and uniqueness theorems by fixed points of operators are investigated. Finally, as applications, we apply the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problems.
