Fixed point belonging to the zero-set of a given function

Abstract

We prove the existence and uniqueness of fixed point belonging to the zero-set of a given function. The results are established in the setting of metric spaces and partial metric spaces. Our approach combines the recent notions of (F,φ)contraction and Z-contraction. The main result allows to deduce, as a particular case, some of the most known results in the literature. An example supports the theory.