This paper deals with the study of \(S\)-curvature, \(E\)-curvature and Berwald scalar curvature for Finsler spaces. More exactly, the author proves that the \(S\)-curvature of a Finsler space vanishes if and only if the \(E\)-curvature vanishes if and only if the Berwald scalar curvature vanishes. This result is obtained in Theorem 2 which contains the following assertion: ``A Finsler space has vanishing mean Berwald curvature if and only if it has vanishing \(S\)-curvature: that is, \(E\) = 0 if and only if \(S\) = 0''. This theorem is proved in Section 4. Also in Section 4, the author extends these results to the case when these objects are isotropic. In this respect, in Theorem 3, he proves that ``\(F\) has isotropic \(S\)-curvature is equivalent with \(F\) has isotropic \(E\)-curvature and also equivalent with \(F\) has isotropic Berwald scalar curvature''. Another interesting result is established in Corollary 3, namely: ``The \(S\)-curvature of a Finsler space is weakly isotropic if and only if it is isotropic.'' These results show us that there is a direct equivalence regarding the vanishing theorems between \(S\)-curvature, \(E\)-curvature and Berwald scalar curvature for Finsler spaces.