  DP-coloring (also known as correspondence coloring) is a generalization of
list coloring developed recently by Dvo\v{r}\'ak and Postle. We introduce and
study $(i,j)$-defective DP-colorings of simple graphs. Let $g_{DP}(i,j,n)$ be
the minimum number of edges in an $n$-vertex DP-$(i,j)$-critical graph. In this
paper we determine sharp bound on $g_{DP}(i,j,n)$ for each $i\geq3$ and $j\geq
2i+1$ for infinitely many $n$.
