doiSerbia

Coupled fixed point theorems for new contractive mixed monotone mappings and applications to integral equations

Işik Hüseyin (Muş Alparslan University, Faculty of Science and Arts, Department of Mathematics, Muş, Turkey + University of Gazi, Faculty of Science, Department of Mathematics, Teknikokullar, Ankara, Turkey)
Türkoğlu Duran (University of Amasya, Faculty of Science and Arts, University of Amasya, Amasya, Turkey + University of Gazi, Faculty of Science, Department of Mathematics, Teknikokullar, Ankara, Turkey)

The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and some other authors and to prove some new coupled fixed point theorems for mappings having a mixed monotone property in a complete metric space endowed with a partial order. Our theorems can be used to investigate a large class of nonlinear problems. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.

Keywords: coupled fixed point, mixed monotone mapping, contractive condition, partially ordered set, integral equation