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

Abstract The manuscript is an extension of the investigations concerning ? -contractions which have been newly proposed in (Jleli and Samet J. Inequal. Appl. 2014:38, 2014). authors generalize notion to case nonlinear $\theta _{b} $ ? b -contraction mappings prove multi...