(q-1,q-2)-quasimetric spaces. Covering mappings and coincidence points

We introduce (q1, q2)-quasimetric spaces and investigate their properties.We study covering mappings from one (q1, q2)-quasimetric space to another and obtain sufficient conditions for the existence of coincidence points of two mappings between such spaces provided that one of them is covering and the other satisfies the Lipschitz condition. These results are extended to multi-valued mappings. We prove that the coincidence points are stable under small perturbations of the mappings.