Unification of several distance functions and a common fixed point result

Abstract In this work, we initiate the notions of dislocated- $A_{b}$ A b -quasi-metric and $A_{b}$ A b -quasi-metric-like spaces. Then we establish the existence of a common fixed point of weakly compatible mappings satisfying a contractive condition on a closed neighborhood of dislocated $A_{b}$ A b -quasi-metric spaces. Some examples are given to show that these spaces are more general than various known comparable metric spaces. Our result unify, complement, and generalize various known results in the literature.