The Banach space m_p(X), for 1 ≤ p

Problem statement: In the theory of Banach spaces one of the problems which describes geometric property of Banach spaces is Banach-Saks Property. In this context we were known many Banach spaces which had this property such as L_p[0, 1] for 1 < p ≤ 2. Approach: Following the sequential structure of the Banach sequence space m_p(X), for 1  ≤ p < 8, defined in^[1], we arrived to describe a geometric property of this Banach spaces. Results: In this note we showed that Banach spaces mp(X), for 1  ≤ p < 8 had the Banach-Saks Property. Conclusion/Recommendations: Based in present approach, we recommend using our method to study the weak Banach-Saks property in sequential Banach spaces.