Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X24201710012-Local derivations on matrix algebras and algebras of measurable operators4945054348210.22034/aot.1612-1074ENShavkat AyupovKarimbergen KudaybergenovAmir AlauadinovJournal Article20161208Let $mathcal{A}$ be a unital Banach algebra such that any Jordan derivation from $mathcal{A}$ into any $mathcal{A}$-bimodule $mathcal{M}$ is a derivation. We prove that any 2-local derivation from the algebra $M_n(mathcal{A})$ into $M_n(mathcal{M}),,(ngeq 3)$ is a derivation. We apply this result to show that any 2-local derivation on the algebra of locally measurable operators affiliated with a von Neumann algebra without direct abelian summands is a derivation.http://www.aot-math.org/article_43482_5c7c7ad78c756b7cccec7aecf018feb2.pdf