2-local $ (\upvarphi, \uppsi) $-Derivations on Finite von Neumann Algebras

In this paper, I introduce the concept of $(\upvarphi, \uppsi)$-finite von Neumann algebras and I show that if $\mathscr{M}$ is a finite and $(\upvarphi, \uppsi)$-finite von Neumann algebra togather with condition $\{ \big( \Delta(u+v)-\Delta(u)-\Delta(v)\big)^{*}\} \subseteq \uppsi(\mathscr{M})$, then each (approximately) 2-local $(\upvarphi, \uppsi)$-derivation $\delta$ on $\mathscr{M}$, is a $(\upvarphi, \uppsi)$-derivation.