Let a metric space. A mapping is called a Caristi’s mapping if there exists a lower semicontinuous function satisfying
for all . W. A. Kirk [Colloq. Math. 36, 81–86 (1976; Zbl 0353.53041)] proved that a metric space is complete if and only if every Caristi’s mapping has a fixed point. A map is said to be a partial metric if for all : (i) ; (ii) ; (iii) , (iv) In this paper the author studies the relationship between the existence of fixed points for Caristi’s type mappings and completeness in a partial metric space.