Fixed point theorems for non-self mappings in symmetric spaces under φ-weak contractive conditions and an application to functional equations in dynamic programming

In this paper, we prove some common fixed point theorems for two pairs of non-self weakly compatible mappings enjoying common limit range property, besides satisfying a generalized φ-weak contractive condition in symmetric spaces. We furnish some illustrative examples to highlight the realized improvements in our results over the corresponding relevant results of the existing literature. We extend our main result to four finite families of mappings in symmetric spaces using the notion of pairwise commuting mappings. Finally, we utilize our results to discuss the existence and uniqueness of solutions of certain system of functional equations arising in dynamic programming.