Comparing convexity in multivariate functions with univariate ones

Question

Suppose I have a function of a single variable: $$ y=f\left(x\right) $$ where $f_{x}>0$ and $f_{xx}>0,$ or that it is a convex function. Now suppose that I have a function of multiple variables: $$ y=g\left(x,z\right) $$ where we know that $g_{x},g_{z},g_{xx},g_{zz}>0$ , such that the function is convex in both of its arguments. I can easily compare the convexity between $f$ and$g$ in $x$ (compare $f_{xx}$and $g_{xx}$), this does not seem correct, because of the presence of $z$ in the $g$ function. Is there a way to compare the degree of convexity in both functions? While in the first case, just looking at $f_{xx}$ is all that you need to know about convexity, is there a summary measure for the function $g$ to summarize the convexity of both arguments in one measure?