Fixed and coincidence point theorems on partial metric spaces with an application

The aim of this paper is to investigate some fixed and co-incidence point theorems in complete, orbitally complete and (T, f)-orbitally complete partial metric spaces under the generalized contractive type conditions of mappings. Moreover, our results generalize and extend the several obtained results in the literature. Additionally some non-trivial examples are demonstrated, and an application has discussed to integral equations.