A discussion on some recent coupled fixed point results via new generalized nonlinear contractive conditions

Abstract

Recently, Samet et al. [34], by using the equivalence of the three basic metrics showed that certain coupled fixed point results can be obtained immediately from the well-known fixed point theorems. In the setting of partially ordered metric spaces, we establish a generalization of the recent coupled fixed/ coincidence point results under new nonlinear contractive conditions. The significant feature of the presented work is that, our obtained results are not the immediate consequence of the already existing results in the literature. Presented work generalizes some of the results of Bhaskar and Lakshmikantham [6], Berinde [7], Choudhury et al. [10], Harjani et al. [17], Jain et al. [21] , Karapinar et al. [22], Luong and Thuan [25], and Rasouli and Bahrampour [30].