  The purpose of this paper is to study infinitesimal H-pseudobialgebra, which
is an associative analogy of Lie H-pseudobialgebra. We first define the
infinitesimal H-pseudobialgebra and investigate some properties of this new
algebraic structure. Then we consider the coboundary infinitesimal
H-pseudobialgebra, which is the subclass of infinitesimal H-pseudobialgebra and
we obtain the associative Yang-Baxter equation over an associative
H-pseudoalgebra. Finally, we found the connection between the (coboundary)
infinitesimal H-pseudobialgebra and the (coboundary) Lie H-pseudobialgebra.
Meanwhile, the relationship between the associative Yang-Baxter equation and
the classical Yang-Baxter equation (over an H-pseudoalgebra) is established.
