Probabilistic \(b\)-suprametric spaces and nonlinear contractions, with an application to \((\zeta_1,\zeta_2)\)-decomposable measures

Abstract

This paper introduces the concept of probabilistic b-suprametric spaces (PbSMS). We conduct a systematic investigation of the fundamental topological properties inherent to these spaces. A key result is the proof of a fixed point theorem for nonlinear Banach-type contractions within the PbSMS framework, which is supported by illustrative examples. Finally, we demonstrate the practical utility of our main result by applying it to the theory of \( (\zeta_1, \zeta_2) \)-decomposable measures.