Let A be an algebra and let X be an A-bimodule. A C−linear mapping d : A → X is called a generalized Jordan derivation if there exists a Jordan derivation (in the usual sense) δ : A → X such that d(a) = ad(a) + δ(a)a for all a ∈ A. The main purpose of this paper to prove the Hyers-Ulam-Rassias stability and superstability of the generalized Jordan derivations.

A theorem of S. Warschawski on the derivative of a holomorphic function mapping conformally the circle onto a simply-connected domain bounded by the piecewise-Lyapunov Jordan curve is extended to domains with a non-Jordan boundary having interior cusps of a certain type. 2000 Mathematics Subject Classification: 3OC35.

We introduced a new nonassociative algebra, namely, left almost algebra, and discussed some of its genetic properties. We discussed the relation of this algebra with flexible algebra, Jordan algebra, and generalized Jordan algebra.

Let A,B be two unital C∗−algebras. We prove that every almost unital almost linear mapping h : A −→ B which satisfies h(3uy + 3yu) = h(3u)h(y) + h(y)h(3u) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2, ..., is a Jordan homomorphism. Also, for a unital C∗−algebra A of real rank zero, every almost unital almost linear continuous mapping h : A −→ B is a Jordan homomorphism when h(3uy + 3yu) = h...

Physically meaningful regions can be modeled by regular open semianalytic sets with bounded boundaries. These sets are named as Yin sets and they form a topological space called the Yin space. Due to the regularity, the Yin sets can be represented by a collection of particular sets of oriented Jordan curves; this collection is referred to as the Jordan space. After defining a meet operation, a ...