On common fixed points that belong to the zero set of a certain function


Erdal Karapinar - Department of Mathematics, Atilim University, ˙Incek, Ankara, 06836, Turkey.
Bessem Samet - Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia.
Priya Shahi - St. Andrews College of Arts, Science and Commerce, St. Dominic Road, Bandra (West), Mumbai 400 050, India.


We provide sufficient conditions under which the set of common fixed points of two self-mappings \(f, g : X \rightarrow X\) is nonempty, and every common fixed point of f and g is the zero of a given function \(\varphi:X \rightarrow [0,\infty)\). Next, we show the usefulness of our obtained result in partial metric fixed point theory.