Fixed-point theorems of φ concave-(−ψ) convex mixed monotone operators and applications ✩

In this paper, φ concave-(−ψ) convex operators are introduced and some new existence and uniqueness theorems of fixed points of mixed monotone operators with such concavity and convexity are obtained. Moreover, some applications to nonlinear integral equations on bounded or unbounded regions are given.  2004 Elsevier Inc. All rights reserved.