Abstract: In this article, we introduce new sequence spaces U(T (x), F, p, u), U(Tw(x), F, p, u) and U(Tw∗ (h), F, p, u) by using Fibonacci matrix and sequence of modulus functions. We make an effort to study some characterizations of weakly unconditionally Cauchy series associated to newly formed sequence spaces. Finally, the barreledness of a normed space Y is characterized by means of weakly∗ unconditionally Cauchy series in Y ∗ .