Coincidence Point Results on Relation Theoretic Fw,Rg-Contractions and Applications

Motivated by the ideas of F-weak contractions and F,Rg-contractions, the notion of Fw,Rg-contractions is introduced and studied in the present paper. The idea is to establish some interesting results for the existence and uniqueness of a coincidence point for these contractions. Further, using an additional condition of weakly compatible mappings, a common fixed-point theorem and a fixed-point result are proved for Fw,Rg-contractions in metric spaces equipped with a transitive binary relation. The results are elaborated by illustrative examples. Some consequences of these results are also deduced in ordered metric spaces and metric spaces endowed with graph. Finally, as an application, the existence of the solution of certain Voltera type integral equations is investigated

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

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

Solving Integral Equations via Hybrid Interpolative ℛℐ-Type Contractions in 𝔟-Metric Spaces

Karapinar et al. established a more general class of contractions, namely, hybrid interpolative Riech Istrǎstescue-type contractions, and presented some results on the platform of metric spaces. This research uses the domain of b-metric spaces to modify this class proficiently. Several interesting fixed-point results are presented by using this new class defined on b-metric space, where the symmetric condition is preserved in this study. Examples are provided for the authentication of proved results. Eventually, an application is also provided in order to comprehend our extensive effort in a better way