This article aims to adopt some notions for mapping f:Xk→X, (where integer k is positive) and to prove the nonlinear-Prešić-type results on metric spaces employing a f-reflexive and locally finitely f-transitive binary relation (not necessarily partial order). The outcomes proven herewith are extended and generalized to several fixed point findings of literature. Lastly, examples are provided to support the applicability of these outcomes.
