Some fixed point theorems in generalized parametric metric spaces and applications to ordinary differential equations

The objective of this work is the construction of Boyd-Wong fixed point theorem' in the setting of generalized parametric metric space and discussion its application on existence criteria of solutions to a second order initial value problem. Also an analogue of Banach type fixed point theorem of generalized parametric metric space is proved and its application on the existence of a solution of first order periodic boundary value differential equation is examined.