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The purpose of present paper is to study the T-tensor of such a Finsler space with the condition L2(α,β)C=β, where α=sqrt(aij(x)yiyj) and β=biyi and get some important theorems. We shall also obtain the condition for such a Finsler space to be a Landsberg space or Berwald space. The notations and terminologies are referred to the monograph [M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha Press, 1986].