Existence and uniqueness of common fixed point in C∗-algebra valued metric space using E. A. and CLR properties.

In this paper, the theorems are given to discussing about two pair of weakly compatible mappings which posses a unique common fixed point of under a certain type of contraction. With the help of E. A. and CLR properties, we also prove a unique common fixed point under certain type contraction for two pairs of mappings. The proved results are helpful to extend and generalize the literature's result. To illustrate our results, some examples are provided in last. [ABSTRACT FROM AUTHOR]