In this paper, we prove some coincidence point theorems for weak C-contractions and K-contractions involving a new auxiliary function in a metric space endowed with a locally $ f $-transitive binary relation. In this context, we generalize some relevant fixed point results in the literature. Further, we give an example to substantiate the utility of our results.

In this article, we prove some coincidence and common fixed point theorems under the relation-theoretic Meir-Keeler contractions in a metric space endowed with a locally finitely -transitive binary relation. Our newly proved results generalize, extend, and sharpen some existing coincidence point as well as fixed point theorems existing in the literature. Moreover, we give some examples to affirm the efficacy of our results.

In this paper, we extend the idea of $\alpha$-$\psi$ contraction mapping to the product spaces by introducing Prešić–Ćirić-type $\alpha$-$\psi$ contractions and utilize them to prove some coincidence and common fixed-point theorems in the context of ordered metric spaces using $\alpha$-admissibility of the mapping. Our newly established results generalize a number of well-known fixed-point theorems from the literature. Moreover, we give some examples that attest to the credibility of our results. Further, we give an application to the nonlinear integral equations, which can be employed to study the existence and uniqueness of solutions to the integral equations.

In this article, we introduce the idea of relation theoretic multivalued Suzuki-generalized nonlinear contractions and utilized the same to prove some fixed point results in a R-complete partial metric space. Our newly proved results are sharpened versions of several known results of the existing literature, which is substantiated by an example. Moreover, the stability of fixed point sets of the multivalued contractions is also discussed. Further, we give an application to the iterated function space.