Common fixed point results of generalized almost rational contraction mappings with an application

In this paper, we introduce the notion of generalized almost rational contraction with respect to a pair of self mappings on a complete metric space. Several common fixed point results for such mappings are proved. Our results extend and unify various results in the existing literature. An example and application to obtain the existence of a common solution of the system of functional equations arising in dynamic programming are also given in order to illustrate the effectiveness of the presented results.