In this paper, we establish the existence and uniqueness of common fixedpoint theorems for self mappings satisfying the common limit range property with re-spect to mappings S and T and common (E.A)-property via the concept of C-classfunctions in b-metric spaces. We furnish two examples to validate our results. Our re-sults improve various results appeared in the current literature. As an application, Weprovide the existence of a solution of an integral equations.