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The main purpose of this paper is to unify and to generalize some common fixed point results in metric spaces with a Q-function (or a w-distance) and the related results in dislocated metric spaces (also called metric-like spaces). First in the setting of dislocated quasi-metric spaces we introduce the notion of weak 0-σ-completeness which is weaker than 0-σ-completeness. By using the new type of completeness, we establish some common fixed point theorems for two self-mappings satisfying a nonlinear contractive condition of Ćirić type. Our results unify and generalize many well-known common fixed point theorems. Finally, we give some further applications of our main results.

A unified view on common fixed point theorems for Ćirić quasi-contraction maps