Some strong coupled coincidence and coupled best proximity results on complete metric spaces

Abstract

Abstract In this paper, the concept of Wardowski’s class of contraction is integrated with that of g-coupling to define some F-contractive type g-couplings. We establish existence results for a coupled coincidence point, a strong coupled coincidence point, and a coupled best proximity point for these couplings within the framework of complete metric space. Additionally, we establish the existence of a coupled coincidence point for multivalued F-contractive type g $\mathfrak{g}$ -coupling. Further, an application of our result with regard to the existence of a system of nonlinear integral equations is discussed.

Keywords

• Coupled fixed point
• Strong coupled fixed point
• Cyclic contraction
• Coupled best proximity points
• Complete metric space
• F-contraction