We deene a residue current of a holomorphic mapping , or more generally a holomorphic section to a holomorphic vector bundle, by means of Cauchy-Fantappie-Leray type formulas , and prove that a holomorphic function that annihilates this current belongs to the corresponding ideal locally. We also prove that the residue current coincides with the Colee-Herrera current in the case of a complete in...

A family of generalized Cauchy distributions, T-Cauchy{Y} family, is proposed using the T-R{Y} framework. The family of distributions is generated using the quantile functions of uniform, exponential, log-logistic, logistic, extreme value, and Fréchet distributions. Several general properties of the T-Cauchy{Y} family are studied in detail including moments, mean deviations and Shannon’s entrop...

A function f ∈ C(Ω) is holomorphic on Ω, if it satisfies the CauchyRiemann equations: ∂̄f = ∑n k=1 ∂f ∂z̄k dz̄k = 0 in Ω. Denote the set of holomorphic functions on Ω by H(Ω). The Bergman projection, B0, is the orthogonal projection of square-integrable functions onto H(Ω)∩L2(Ω). Since the Cauchy-Riemann operator, ∂̄ above, extends naturally to act on higher order forms, we can as well define Bergm...

We study new sequence spaces associated to sequences in normed spaces and the band matrix F̂ defined by the Fibonacci sequence. We give some characterizations of continuous linear operators and weakly unconditionally Cauchy series by means of completeness of the new sequence spaces. Also, we characterize the barreledness of a normed space via weakly∗ unconditionally Cauchy series in [Formula: se...

The purpose of this paper is to prove that every sequence of closed approximable measures defined on the Borelfield of a normal topological space with values in an abelian topological group is Cauchy convergent for all Borel sets if it is Cauchy convergent for all regular open sets. In particular every sequence of measures on the Borel-field of a perfectly normal topological space which is Cauc...

Let (X, d) be a metric space. The goal of these notes is to construct a complete metric space which contains X as a subspace and which is the “smallest” space with respect to these two properties. The resulting space will be denoted by X and will be called the completion of X with respect to d. The hard part is that we have nothing to work with except X itself, and somehow it seems we have to p...

Convergence with respect to a valuation is discussed as convergence of a Cauchy sequence. Cauchy sequences of polynomials are defined. They are used to formalize Hensel’s lemma.

Let DN be the linear space spanned by the ej for j ≤ N then if the orthogonal decomposition H = DN ⊕D⊥ N gives u = u′ + u′′ and the distance d(u,DN ) = ‖u′′‖ so the finite dimensional approximation property follows from (2). Conversely, suppose that K is closed and bounded and has the FDAP. By the assumed boundedness, any sequence in K has a weakly convergent subsequence. Denote such a sequence...

and Applied Analysis 3 Definition 2.2 Kramosil and Michálek 3 . The triple X,M, ∗ is called a fuzzy metric space if X is an arbitrary set, ∗ is a continuous t-norm, andM is a fuzzy set onX×X× 0,∞ satisfying the following conditions: for all x, y, z ∈ X and s, t > 0, FM-1 M x, y, 0 0, FM-2 M x, y, t 1 if and only if x y, FM-3 M x, y, t M y, x, t , FM-4 M x, y, t ∗M y, z, s ≤ M x, z, t s , FM-5 a...

The aim of this paper is to introduce the concept of convergence of a sequence on hypernormed spaces and establish a few basic properties of convergent sequences and Cauchy sequences on hypernormed spaces. Also we have established a necessary and sufficient condition for a Cauchy sequence to be convergent sequence in this spaces. In fact, also it has been shown that limit of a convergent sequen...