Some φ-coupled fixed point results via modified F-control function's concept in metric spaces and its applications

The aim of this paper is to propose a new φ-coupled fixed point theorem for a mixed monotone mapping in a metric space, which is taken no account of the continuity of the mapping. To this end, we introduce the notions of φ-coupled fixed point and modified F-control function. Our obtained results are applied to derive some φ-coupled fixed point theorems in partial metric spaces and quasi-metric spaces, respectively. Some applications to matrix equations and integral equations are also presented so as to illustrate our results.