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Description:
We consider the sum of squared logarithms inequality and investigate possible connections with the theory of majorization. We also discuss alternative sufficient conditions on two sets of vectors a,b∈Rn+ so that ∑ni=1(logai)2 ≤ ∑ni=1(logbi)2. Generalizations of some inequalities from information theory are obtained, including a generalized information inequality and a generalized log sum inequality, which states for a,b∈Rn+ and k1,.,kn∈[0,∞): ∑ni=1ailog∏ms=1(aibi+ks) ≥ log∏ms=1(1+ks).