Virtualized Delta moves for virtual knots and links

We introduce a local deformation called the virtualized $\mathrm{\Delta }$-move for virtual knots and links. We prove that the virtualized $\mathrm{\Delta }$-move is an unknotting operation for virtual knots. Furthermore we give a necessary and sufficient condition for two virtual links to be related by a finite sequence of virtualized $\mathrm{\Delta }$-moves.