On some λ difference sequence spaces of fractional order

In the present paper, the difference sequence spaces $c{s}_0^{\lambda }\left(\Delta \right),c{s}^{\lambda }\left(\Delta \right)$ and bs^λ(Δ) of nonabsolute type are generalized by introducing a generalized Λ difference operator $\Lambda \left({\Delta }^{\left(\stackrel{?}{\alpha }\right)}\right)$. Also, their Schauder basis are calculated and α-, β- and γ-duals of these spaces are investigated. Finally, some matrix transformations between these spaces and the basic sequence spaces ?_p, c and c₀ are characterized, where 1 ≤ p ≤ ∞.     

On some geometric properties of generalized Orlicz–Lorentz function spaces

In this article we continue investigations concerning generalized Orlicz–Lorentz function spaces _Λφ${\Lambda }_{\phi }$ initiated in the papers (Foralewski, 2011)  and  (cf. also (Foralewski, 2008)  and ). First, it is shown that modular _?φ${?}_{\phi }$ is orthogonally subadditive. Next, monotonicity properties are considered. In order to get sufficient conditions for uniform monotonicity of the space _Λφ${\Lambda }_{\phi }$ a strong condition of _Δ2${\Delta }_2$ type and the notion of regularity of the generated Musielak–Orlicz function φ$\phi$ are introduced. Finally, criteria for non-squareness of _Λφ${\Lambda }_{\phi }$ are presented.     

On ∑-products of semi-stratifiable spaces

Let ∑ be a ∑-product of semi-stratifiable spaces as in our title. First, we consider when ∑ is normal. Secondly, we consider when ∑ is collectionwise normal if it is normal. Moreover, it is shown that ∑ is subnormal.     

Extreme points and rotundity of Orlicz-Musielak sequence spaces

A.Kaminska and H.Hudzik[1-10] present a series of work concerning geometry ofsequence Orlicz-Musielak spaces. This paper continues their work, to give a character of extremepoints of the unit balls of sequence Orlicz-Musielak spaces epuipped with Luxemburg norm. Fromwhich a criterion of rotundity is obtained immediately.     

On a Volume Parameter of Banach spaces

Having discussed the parameter in [5] we introduce in this paper a volume parameter We give some properties of it, and obtain that P_3(x)<4 if X is 2UR, and that X is a super-reflexive Banach space if p_3(x)<4.     

On characterizations of isometries on function spaces

The paper gives characterization for an isometric isomorphism on little Bloch space, VMOA and holomorphic Besov space over the unit ball B_n in C~n.     

On the ℂ-differentiability of mappings of Banach spaces

We study the monogeneity conditions for -differentiable mappings of domains of a Banach space and establish criteria of -differentiability of a mapping at a point.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1336–1342, October, 1994.     

On the spaces C k (ℝ) ∩ L p (ℝ)

We show that the Fréchet-Sobolev spaces C(ℝ) ∩ L ^p (ℝ) and C ^k (ℝ) ∩ L ^p (ℝ) are not isomorphic for p ≠ 2 and k ∈ ℕ. Research supported by the Italian MURST.     

On the homotopy type of Poincaré spaces

We study the homotopy type of finite-oriented Poincaré spaces (and, in particular, of closed topological manifolds) in even dimension. Our results relate polarized homotopy types over a stage of the Postnikov tower with the concept of CW-tower of categories due to Baues. This fact allows us to obtain a new formula for the top-dimensional obstruction for extending maps to homotopy equivalences. Then we complete the paper with an algebraic characterization of high-dimensional handlebodies. Received: April 14, 1999?Published online: October 2, 2001     

Inclusions of Waterman–Shiba spaces into generalized Wiener classes

The characterization of the inclusion of Waterman–Shiba spaces ΛBV^(p)$\Lambda {\mathit{BV}}^{(p)}$ into generalized Wiener classes of functions BV(q;δ)$\mathit{BV}(q;\delta )$ is given. It uses a new and shorter proof and extends an earlier result of U. Goginava.     

On ℒ-starcompact spaces

A space X is ?-starcompact if for every open cover of X, there exists a Lindelöf subset L of X such that St(L, ) = X. We clarify the relations between ?-starcompact spaces and other related spaces and investigate topological properties of ?-starcompact spaces. A question of Hiremath     

μ-Separations in generalized topological spaces

This paper takes some investigations on generalized topological spaces with some μ- separations. Some characterizations of μTi-spaces for i = 0,1,2,3,4, μTD-spaces and μR0-spaces are obtained and some relations among these spaces are established.     

On the convergence of generalized Padé approximants

Letf be an analytic function with all its singularities in a compact set \(E_f \subset \bar C\) of (logarithmic) capacity zero. The function may have branch points. The convergence of generalized (multipoint) Padé approximants to this type of function is investigated. For appropriately selected schemes of interpolation points, it is shown that close-to-diagonal sequences of generalized Padé approximants converge in capacity tof in a certain domain that can be characterized by the property of the minimal condenser capacity. Using a pole elimination procedure, another set of rational approximants tof is derived from the considered generalized Padé approximants. These new approximants converge uniformly on a given continuum \(V \subset \bar C\backslash E_f\) with a rate of convergence that has been conjectured to be best possible. The continuumV is assumed not to divide the complex plane.     

ζ μ -sets in generalized topological spaces

We define ζ _μ -sets, (ζ,μ)-closed sets and generalized ζ _μ -sets in a generalized topological space and investigate properties of several low separation axioms of generalized topologies constructed by the families of these sets. Characterizations of some properties of (ζ,μ)-R ₀ and (ζ,μ)-R ₁ generalized topological spaces will be given.