ISOMORPHISMS AND GENERALIZED DERIVATIONS IN PROPER CQ∗ -ALGEBRAS

Isomorphisms and Generalized Derivations in Proper Cq∗-algebras

In this paper, we prove the Hyers-Ulam-Rassias stability of homomorphisms in proper CQ∗-algebras and of generalized derivations on proper CQ∗-algebras for the following Cauchy-Jensen additive mappings: f ( x + y + z 2 ) + f ( x− y + z 2 ) = f(x) + f(z), f ( x + y + z 2 ) − f ( x− y + z 2 ) = f(y), 2f ( x + y + z 2 ) = f(x) + f(y) + f(z), which were introduced and investigated in [3, 30]. This i...

Proper CQ∗-ternary algebras

In this paper, modifying the construction of a C∗-ternary algebra from a given C∗-algebra, we define a proper CQ∗-ternary algebra from a given proper CQ∗-algebra. We investigate homomorphisms in proper CQ∗-ternary algebras and derivations on proper CQ∗-ternary algebras associated with the Cauchy functional inequality ‖f(x) + f(y) + f(z)‖ ≤ ‖f(x+ y + z)‖. We moreover prove the Hyers-Ulam stabili...

MODULE GENERALIZED DERIVATIONS ON TRIANGULAUR BANACH ALGEBRAS

Let $A_1$, $A_2$ be unital Banach algebras and $X$ be an $A_1$-$A_2$- module. Applying the concept of module maps, (inner) modulegeneralized derivations and  generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $A_i$ into the dual space $A^*_i$ (for$i=1,2$) and such derivations  from  the triangular Banach algebraof t...

Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras

On Generalized Left Derivations in BCI-Algebras

In the present paper, we introduce the notion of generalized left derivation of a BCI-algebra X , construct several examples, and investigate related properties. Also establish some results on regular generalized left derivation. Furthermore, for a generalized left derivation H, the concept of a H-invariant generalized left derivation is introduced, and examples are discussed. Using this concep...