# How to prove pseudo-convexity of a discrete function?

Given a general function $$f:\Bbb Z\to\Bbb R$$ is there a simple way to verify whether $$f(x)$$ is pseudo-convex or not?

However, in your case your domain is $$\mathbb{Z}$$, therefore derivatives are generally not defined, and neither is the concept of (pseudo)convexity.
You can show whether the relaxed $$f:\mathbb{R}\rightarrow \mathbb{R}$$ is pseudo-convex, but the concept is not defined in the integral domain. In a way, this directly answers your question: $$f:\mathbb{Z}\rightarrow \mathbb{R}$$ can not be pseudo-convex.