SOME ACHIEVEMENTS ON TWO VARIABLES $\sigma$derivations
Abstract
Let
B and A be two Banach algebras and M be a Banach B
: A ! B

: A × A ! M is called a two variables derivation whenever (ab, c

(a, c)(b)+(a)(b, c) and (a, bc) = (a, b)(c)+(b)(a, c) for all a, b, c 2 A
A and B are unital and  : A × A ! B
derivation such that (1, a0) = 1 for some a0 2 A then
is symmetric, i.e.
(a, b) = (b, a
: A ! B such that (a, b) = (ab)(a0)−1
.
) and there exists a unital homomorphism

is atwo variables
.In this paper, we prove that if
) =
is a linear mapping. A bilinear map
bimodule.Suppose that
Keywords
derivation; two variables derivation; two variables derivation;
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