  In this paper, we define two types of strongly decomposable positivity, which
serve as generalizations of (dual) Nakano positivity and are stronger than the
decomposable positivity introduced by S. Finski. We provide the criteria for
strongly decomposable positivity of type I and type II and prove that the Schur
forms of a strongly decomposable positive vector bundle of type I are weakly
positive, while the Schur forms of a strongly decomposable positive vector
bundle of type II are positive. These answer a question of Griffiths
affirmatively for strongly decomposably positive vector bundles. Consequently,
we present an algebraic proof of the positivity of Schur forms for (dual)
Nakano positive vector bundles, which was initially proven by S. Finski.
