Fixed point theorems for τ‐φ‐concave operators and applications

In this paper, by introducing $\tau \text{–}\phi$ ‐concave operators and using the properties of cones and monotone iterative technique, some new existence and uniqueness theorems of fixed points for increasing operators with such concavity are established under more extensive conditions in ordered Banach spaces. As an application, we study the existence and uniqueness of positive solutions of generalized three‐point boundary value problems for second order differential equations. The results obtained here improve and generalize many known results.