We prove the generalized Hyers-Ulam-Rassias stability of a partitioned functional equation. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with partitioned functional equations in Banach algebras.

In this paper the multi-valued versions of some well-known hybrid fixed point theorems of Dhage [6, 7] in Banach algebras are proved. As an application, an existence theorem for a certain integral inclusion in Banach algebras is proved.

‎ Let $(X,d)$ be a metric space and $Jsubseteq (0,infty)$ be a nonempty set. We study the structure of the arbitrary intersection of vector-valued Lipschitz algebras, and define a special Banach subalgebra of $cap{Lip_gamma (X,E):gammain J}$, where $E$ is a Banach algebra, denoted by $ILip_J (X,E)$. Mainly, we investigate $C-$character amenability of $ILip_J (X,E)$.

several representations of the generalized drazin inverse of an anti-triangular block matrix in banach algebra are given in terms of the generalized banachiewicz--schur form.

We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in C∗-algebras is consider...

using fixed pointmethods, we investigate approximately higher ternary jordan derivations in banach ternaty algebras via the cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$

A class of algebras is introduced that includes the unital Banach algebras over the complex numbers. Commutator results are proved for such algebras and used to establish spectral properties of certain elements of Banach algebras. 1. Introduction. In this note, we introduce a condition on an algebra motivated by the situation in which Schur's lemma [S1] is applicable. We say that algebras satis...

The origin of Korovkin Approximation theory is the classical theorem of P.P. Korovkin (1953),which says that for a sequence (Tn) of positive linear operators on C[a, b], in order to conclude the uniform convergence of Tnf to f for all f ∈ C[a, b], it suffices to check the uniform convergence only for the three functions f ∈ {1, x, x2}. Starting from this beautiful result many mathematicians hav...

The notions of nil, nilpotent or PI-rings (= rings satisfying a polynomial identity) play an important role in the ring theory (see e.g. [8], [11], [20]). Banach algebras with these properties have been studied considerably less and the existing results are scattered in literature. The only exception is the work of Krupnik [13], where the Gelfand theory of Banach PI-algebras is presented. Howev...