Abstract
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.
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