All metric fixed point theorems hold for quasi-metric spaces
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Banach contraction, fixed point, fixed point theorem, metric space, quasi- metric, maximal element. Mathematics Subject Classification: 06A75, 47H10, 54E35, 54H25, 58E30, 65K10Abstract
Our aim in this article is to show that all metric fixed point theorems hold for quasi-metric spaces (X, δ) (without symmetry). In fact, we show some well-known theorems on metric spaces hold for quasi-metric spaces from the beginning. We check this fact for the Banach contraction principle, the Covitz-Nadler fixed point theorem, the Rus-Hicks-Rhoades fixed point theorem, and others. In
these theorems the concepts of continuity and completeness can be replaced by orbital continuity and T-orbital completeness for a selfmap T, respectively.Consequently, we improve and generalize the basic known theorems in the metric fixed point theory.
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