S-Contractive Mappings on Vector-Valued White Noise Functional Space and Their Applications

Abstract

In this paper, we propose a new notion, which we name S-contractive mapping, in a framework of vector-valued white noise functionals Wω⊗N⊂Γ(H)⊗K⊂(Wω⊗N)*. And we give concrete definitions of S-contractive mappings for vector-valued white noise functionals. We establish the fixed-point theorems of S-contractive mappings. As applications, by applying the fixed-point theorems of generalized S-contractive mappings, we prove the existence and uniqueness of a generalized form of differential equations of vector-valued white noise functionals with weak conditions and investigate Wick-type differential equations of vector-valued white noise functionals with generalized conditions.