New fixed points of mixed monotone operators with applications to nonlinear integral equations

Abstract

In this paper, first we recall and present some basic results about cone and partial order within the framework of Banach spaces. Next, by means of the properties of cone and monotone iterative techniques, some new fixed point theorems of mixed monotone operators with certain concavity and convexity are obtained without any compactness or continuity condition. Further, the main results are applied to two classes of nonlinear functional integral equations on unbounded regions. Our results extend and generalize previous findings.