The generalized and extended uncertainty principles affect the Newtonian gravity and also the
geometry of the thermodynamic phase space. Under the influence of the latter, the energy–
temperature relation of ideal gas may change. Moreover, it seems that the Newtonian gravity
is modified in the framework of the R´enyi entropy formalism motivated by both the longrange
nature of gravity and the extended uncertainty principle. Here, the consequences of
employing the generalized and extended uncertainty principles, instead of the Heisenberg
uncertainty principle, on the Jeans mass are studied. The results ofworking in theR´enyi entropy
formalism are also addressed. It is shown that unlike the extended uncertainty principle and
the R´enyi entropy formalism that lead to the same increase in the Jeans mass, the generalized
uncertainty principle can decrease it. The latter means that a cloud with mass smaller than the
standard Jeans mass, obtained in the framework of the Newtonian gravity, may also undergo
the gravitational collapse process.