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

Volume 10, Issue 7, pp 3447--3455 Publication Date: July 21, 2017       Article History
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### Authors

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.

### Abstract

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.

### Keywords

• $\varphi$ -admissibility
• common fixed point
• zero set
• partial metric.

•  54H25
•  47H10

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