Some Fixed Point Results on Generalized Weak Contractions in Partial Metric Spaces With an Application

In this paper, we consider generalized \(\tau\)-\(\psi\)-\(\varphi\) weak contraction and generalized \(\tau\)-\(\varphi\) weak contraction mappings in the setting of partial metric spaces and verify the existence of a fixed point on such spaces. Our results extend and strengthen various known results in this direction. We present an example showing the significance of our result. We also show that our result can be applied to the existence of solutions of a differential equation.