Unique common fixed point theorem using simulation function fulfilling common limit in the range property

In the current research paper we have defined rationalized Ξ-contraction for four mappings. In b-metric, using simulation function, for rationalized Ξ-contraction fulfilling the weakly compatible condition for four mappings in pairs, fulfilling conjoint limit range property, a unique common fixed point theorem has been proved. The conclusion has been tested by not using the situation of completeness for b-metric space. The outcome is an improvement and generalization of [2, 4, 6] existing in metric space and b-metric spaces. To back-up the result a supporting example is also discussed.