A Fixed Point Theorem with Application to a Class of Integral Equations

The notion of dualistic Geraghty Contraction is intro- duced. A new fixed point theorem is proved in the settings of complete dualistic partial metric spaces. The counterpart theorem provided in partial metric spaces is retrieved as a particular case of our new re- sults. We give example to prove that the contractive conditions in the statement of our new fixed point theorem can not be replaced by those contractive conditions in the statement of the partial metric counter- part fixed point theorem. Moreover, we give an application of our fixed point theorem to show the existence of solution of integral equations.