On (ψ,ϕ)(ψ,ϕ)-weakly contractive condition in partially ordered metric spaces

Recently, Heman Kumar Nashine and Bessem Samet [H.K. Nashine, B. Samet, Fixed point results for mappings satisfying (ψ,ϕ)(ψ,ϕ)-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 2201–2209] studied some coincidence fixed point and common fixed point theorems for two mappings satisfying (ψ,ϕ)(ψ,ϕ)-weakly contractive condition in an ordered complete metric space. In the present paper, we study some coincidence fixed point and common fixed point theorems for three mappings S,TS,T and RR satisfying (ψ,ϕ)(ψ,ϕ)-weakly contractive condition in an ordered complete metric space, where the mappings SS and TT are assumed to be weakly increasing with respect to RR. Our results generalize several well-known results in the literature.