Fixed point theorems for τ - φ-concave-convex operators and applications

In this paper, we introduce the concept of a tau - phi-concave-convex operator. Meanwhile by the properties of cone and monotone iterative technique, we prove some new existence and uniqueness theorems of fixed points for mixed monotone operators under more extensive conditions in ordered Banach spaces. Finally, we apple the results to a nonlinear Hammerstein integral equation. The results given in this work generalize and extend some known results (e.g., [Z. Q. Zhao, Existence and uniqueness of fixed points for some mixed monotone operators. Nonlinear Anal., 73 (2010)1481-1490.]).