Existence of coincidence point for weakly increasing mappings satisfies \((\psi,\phi)\)-weakly contractive condition in partially ordered metric spaces (Q2224132)

Summary: \textit{H. K. Nashine} and \textit{B. Samet} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 6, 2201--2209 (2011; Zbl 1208.41014)] showed some common fixed point theorems for two mappings satisfying \((\psi,\phi)\) weakly contractive condition in an ordered complete metric space. Further, this result was extended by \textit{W. Shatanawi} and \textit{B. Samet} [Comput. Math. Appl. 62, No. 8, 3204--3214 (2011; Zbl 1232.54041)] to three mappings \(S, T\) and \(R\) satisfying a 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 apply it to prove a coincidence point theorem under a generalised contractive principle.