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In 2011, H.K. Nashine and B. Samet (2011) showed some common fixed point theorems for two mappings satisfying (ψ, φ)-weakly contractive condition in an ordered complete metric space. Further, this result was extended by W. Shatanawi and B.Samet (2011) to three mappings S,T and R satisfying weakly contractive condition in partially ordered metric spaces in which S,T were assumed to be weakly increasing with respect to R. In the present paper, we define weakly increasing mapping for four self maps and then implant it to prove the coincidence point theorem satisfying a generalized contractive principle.