Common Fixed Point Results for Asymptotic Quasi-Contraction Mappings in Quasi-Metric Spaces

In this article, two new classes of pairs {T, f} consisting of an asymptotic quasi-contraction
T with respect to a map f are introduced. The existence and uniqueness of the common fixed
point of such pairs {T, f} is then established in the context of a quasi-metric space X, when
T and f are weakly compatible. The theorems obtained rely on some conditions on the orbit
OT ,f (x, ∞) of T at points x ∈ X with respect to f, and are in fact, improvements of previously
known results in the literature of metric-types. An example is given to validate the results
obtained.