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We give a characterization of relative Ding stable toric Fano manifolds interms of the behavior of the modified Ding functional. We call thecorresponding behavior of the modified Ding functional the pseudo-boundednessfrom below. We also discuss the pseudo-boundedness of the Ding / Mabuchifunctional of general Fano manifolds.

Remarks on modified Ding functional for toric Fano manifolds