Generalized large triangle–perimeter contractions with time scaling in fuzzy \(b\)-metric spaces

Abstract

In this paper, we propose a new class of generalized large triangle–perimeter contractions for single-valued mappings in fuzzy b-metric spaces. The proposed contraction is based on a hybrid geometric functional involving three points and incorporates a time-scaling mechanism. This approach allows us to study mappings that may fail to be contractive at a fixed time parameter but exhibit contractive behavior when observed at varying time scales. We establish a fixed point result confirming the existence and uniqueness of fixed points in complete fuzzy b-metric spaces. The proof technique significantly differs from classical approaches by utilizing time iteration and fuzzy geometric decay mechanism. An application to a nonlinear Volterra-type integral equation with delay is also presented.