A new approach to establish the existence of coincidence point in $C^*$-algebra valued metric space

Abstract

In the present manuscript, we introduce a new approach to establish the existence of a coincidence point for two pairs of compatible and weakly compatible mappings for generalised $(\psi_\mathbb{B}, \phi_\mathbb{B})$-weakly contraction using the $C$-class function in ordered $C^*$-algebra valued metric space. The proved results extend and generalize some of the results in the literature. Some examples are illustrated to support the usability of our results.