Well-Posedness Scheme for Coupled Fixed-Point Problems Using Generalized Contractions

Abstract

In this study, we present a more general class of rational-type contractions in the domain of Hilbert spaces, along with a novel coupled implicit relation. We develop several intriguing results and consequences for the existence of unique coupled fixed points. Further, we investigate a necessary condition that guarantees the well-posedness of a coupled fixed-point problem of self-mappings in Hilbert spaces. Some new observations proposed in this research broaden and extend previously published results in the literature.

Keywords

• Hilbert spaces
• asymptotically regular sequences
• coupled implicit relations
• coupled fixed points
• common coupled fixed points
• well-posedness