Coupled Fixed Points in (q1, q2)-Quasi-Metric Spaces

This paper presents a new coupled fixed-point theorem for a pair of set-valued mappings acting on the Cartesian product of (m1, m2)- and (n1, n2)-quasi-metric spaces. Within the general, non-symmetric quasi-metric setting, we establish the existence of an approximate coupled fixed point. Moreover, under the additional assumption of q0-symmetry, we guarantee the existence of a coupled fixed point. Together, these results extend and unify several known theorems in fixed-point theory for quasi-metric and asymmetric spaces. We illustrate the obtained results regarding fixed points when the underlying space is equipped with a graph structure and, thus, sufficient conditions are found to guarantee the existence of a subgraph with a loop with a length greater than or equal to 2.