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 ...

In this paper, we prove that every Pre A∗-algebra A with 1 is isomorphic to the Pre A∗-algebra of all global sections of a sheaf of indecomposable Pre A∗-algebra over Boolean space and that sheaf of indecomposable Pre A∗-algebra with 1 over Boolean space is isomorphic to the sheaf obtained from the Pre A∗-algebra of all sections of the sheaf. Copyright c © 2011 Yang’s Scientific Research Instit...

We introduce Banach algebras arising from tensor norms. By these Banach algebras we make Arensregular Banach algebras such that tensor product becomes irregular, where is tensor norm. Weillustrate injective tensor product, does not preserve bounded approximate identity and it is notalgebra norm.

(1.1) |f(a)− f(b)| ≤ L |a− b| for every pair of points a, b ∈ A. We also say that a function is Lipschitz if it is L-Lipschitz for some L. The Lipschitz condition as given in (1.1) is a purely metric condition; it makes sense for functions from one metric space to another. In these lectures, we concentrate on the theory of Lipschitz functions in Euclidean spaces. In Section 2, we study extensio...

We study algebraic neural networks (AlgNNs) with commutative algebras which unify diverse architectures such as Euclidean convolutional networks, graph and group under the umbrella of signal processing. An AlgNN is a stacked layered information processing structure where each layer conformed by an algebra, vector space homomorphism between algebra endomorphisms space. Signals are modeled elemen...

In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...

We show that if a distribution is locally spanned by Lipschitz vector fields and is involutive a.e., then it is uniquely integrable giving rise to a Lipschitz foliation with leaves of class C1,Lip. As a consequence, we show that every codimension-one Anosov flow on a compact manifold of dimension > 3 such that the sum of its strong distributions is Lipschitz, admits a global cross section. The ...

We prove that RS-BL-algebras are MV-algebras.

This paper is the first of a two part series. In this paper, we first prove that the variety of dually quasi-De Morgan Stone semi-Heyting algebras of level 1 satisfies the strongly blended $lor$-De Morgan law introduced in cite{Sa12}. Then, using this result and the results of cite{Sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) ...