TY - JOUR
AU - Sehie Park,
PY - 2023/11/03
Y2 - 2024/06/15
TI - All metric fixed point theorems hold for quasi-metric spaces
JF - Results in Nonlinear Analysis
JA - Results in Nonlinear Analysis
VL - 6
IS - 4
SE - Articles
DO -
UR - https://nonlinear-analysis.com/index.php/pub/article/view/356
SP - 116–127
AB - <p>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<br>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.</p>
ER -