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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 Lp[0, 1] for 1 Approach: Following the sequential structure of the Banach sequence space mp(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

The Banach space m<sub>p</sub>(X), for 1 ≤ p <8 has the Banach-Saks Property