In the present paper, we employ the notion of w ‐distance to prove a large Kannan‐type contraction inequality in metric spaces. The notion of a coupled large Kannan contraction is introduced, and by using the Geraghty‐type control function, we derive fixed point results in metric spaces with and without partial order. The control function utilized is a combination of two simultaneous contractive conditions integrated with the w‐distance. Some corollaries of the main theorems are presented. To validate our findings, we provide an illustrative example and also an application to the solution of a system of coupled integral equations.
Chakraborty et al. (Thu,) studied this question.