Additive property for the generalized Zhou inverse in a Banach algebra

Some additive results for the generalized Drazin inverse in a Banach algebra

Additive results for the generalized Drazin inverse in a Banach algebra

In this paper we investigate additive properties of the generalized Drazin inverse in a Banach algebra. We find some new conditions under which the generalized Drazin inverse of the sum a + b could be explicitly expressed in terms of a, a, b, b. Also, some recent results of Castro and Koliha (Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), 1085-1097) are extended. 2000 Mathematics Subject Classif...

Ela Some Additive Results for the Generalized Drazin Inverse in a Banach Algebra

In this note, additive results are presented for the generalized Drazin inverse in Banach algebra. Necessary and sufficient conditions are given for the generalized Drazin invertibility of the sum of two commuting generalized Drazin invertible elements. These results are a generalization of the results from the paper [C.Y. Deng and Y. Wei. New additive results for the generalized Drazin inverse...

On the (p, q) outer generalized inverse in Banach algebra

In this note, the (p, q) outer generalized inverse in Banach algebra is considered, a new representation based on the (1, 5) inverse is presented. Also, we construct an iterative method for computing the (p, q) outer generalized inverse in Banach algebra. 2000 Mathematics Subject Classification: 15A09

Generalized additive functional inequalities in Banach algebras

Using the Hyers-Ulam-Rassias stability method, weinvestigate isomorphisms in Banach algebras and derivations onBanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphismsin Banach algebras and of derivations on Banach ...