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In this paper, by using the weighted geometric mean G(n,t) and the weighted arith- metic one A(n,t) due to Lawson-Lim for each t ∈ (0,1), we investigate n-variable versions of a complement of the Golden-Thompson-Segal type inequality due to Ando-Hiai: Let H1,H2,···,Hn be selfadjoint operators such that mHi M for i= 1,2,···,n and some scalars m M.T hen S(e p(M−m) ) − 2 pG(n,t)(e pH1 ,···,e pHn) 1 p

The Golden-Thompson-Segal type inequalities related to the weighted geometric mean due to Lawson-Lim