Name for a nonlinear version of bilinear form

Question

A map $b:X \times Y \to \mathbb{R}$ is called a bilinear form if $b$ is linear in both arguments.

Is there a name for a form $b$ which is linear in only one argument and may be nonlinear in the other?

Answer 1

It appears that when $X = \mathbb{R}$ this is referred to as being Quasilinear:

In economics and consumer theory, quasilinear utility functions are linear in one argument, generally the numeraire. This utility function has the representation $u(x_1, x_2, \ldots, x_n) = x_1 + \theta (x_2, \ldots, x_n)$.