What's the name of a function of the form $y(x;p) = p f(x) + (1-p) g(x)$?

Question

Is there a name for a function of the form $y(x;p) = p f(x) + (1-p) g(x)$, where $p$ is some scalar between 0 and 1, and $f$ and $g$ are functions?

Answer 1

It's a convex combination of $f$ and $g$. For more information see http://en.wikipedia.org/wiki/Convex_combination.

If $f$ and $g$ are differentiable, then so is $y$ and the derivative with respect to $x$ is given by $pf'(x)+(1-p)g'(x)$, so the derivative of a convex combination is the convex combination of the individual derivatives.