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In this paper, we give refinements for the  G -majorization triangle inequalitywith vectorsof an Eaton triple and normal map. For instance, we establish refinements for the majorization Ky Fan's eigenvalue inequalitywith Hermitian matrices  x  and  y  and the eigenvalue operator. Likewise, we show refinements for the weak majorization Ky Fan's singular value inequalitywith complex matrices  x  and  y , wherestands for the singular values operator. In particular, we recover original Maligranda's refinement of the norm triangle inequality.

On Maligranda like inequalities for G -majorization