Fixed point theory in partial metric spaces via φ-fixed point’s concept in metric spaces

Let X be a non-empty set. We say that an element x∈X is a φ-fixed point of T, where φ:X→[0,∞) and T:X→X, if x is a fixed point of T and φ(x)=0. In this paper, we establish some existence results of φ-fixed points for various classes of operators in the case, where X is endowed with a metric d. The obtained results are used to deduce some fixed point theorems in the case where X is endowed with a partial metric p.