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

The notions of dualistic Geraghty Contraction is intoduced. 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 results. 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 counterpart fixed point theorem. Moreover, we give application of our fixed point theorem to show the existence of solution of integral equations.