Some coupled common fixed point theorems for a pair of mappings satisfying a contractive condition of rational type without monotonicity

The purpose of this paper is to establish some coupled coincidence pointtheorems for a pair of mappings without mixed monotone property satisfying a contractivecondition of rational type in the framework of partially ordered metric spaces. Also, wepresent a result on the existence and uniqueness of coupled common fixed points. Theresults presented in the paper generalize and extend several well-known results in theliterature.