Let \((X,p)\) be a partial metric space and \(p^s(x,y):= 2p(x,y)-p(x,x)-p(y,y) \) the metric on \(X\) generated by \(p\). In this paper the authors study the following problems: If \(T:(X,p) \to (X,p) \) is a generalized contraction, which condition satisfies \(T\) with respect to \(p^s\)? How use fixed point theorems in a metric space \((X,p^s)\) to give analogous fixed point results in a partial metric space \((X,p)\)?