Generalized difference sequence spaces on seminormed space defined by Orlicz functions

In this paper we define the sequence space ℓ _M (Δ ^m , p, q, s) on a seminormed complex linear space by using an Orlicz function. We study its different algebraic and topological properties like solidness, symmetricity, monotonicity, convergence free etc. We prove some inclusion relations involving ℓ _M (Δ ^m , p, q, s).      

On some new generalized difference sequence spaces on seminormed spaces defined by a sequence of Orlicz functions

In this paper we define the sequence space ℓ _M (Δ _υ ^m , p, q, s) on a seminormed complex linear space, by using a sequence of Orlicz functions. We study some algebraic and topological properties. We prove some inclusion relations involving ℓ _M (Δ _υ ^m , p, q, s). spaces     

The conjugate of the difference of convex functions

Given an arbitrary functiong and a convex functionh, we derive the expression of the conjugate ofg —h via a simple proof.     

Applications of utility functions defined on quasi-metric spaces

A quasi-metric space (X,d) is called sup-separable if (X,d^s) is a separable metric space, where d^s(x,y)=max{d(x,y),d(y,x)} for all x,y∈X. We characterize those preferences, defined on a sup-separable quasi-metric space, for which there is a semi-Lipschitz utility function. We deduce from our results that several interesting examples of quasi-metric spaces which appear in different fields of theoretical computer science admit semi-Lipschitz utility functions. We also apply our methods to the study of certain kinds of dynamical systems defined on quasi-metric spaces.     

Some multiplier generalized difference sequence spaces over n-normed spaces defined by a Musielak-Orlicz function

In the present paper, we introduce some multiplier sequence spaces over n-normed spaces defined by a Musielak-Orlicz functionM = (M _k ). We also study some topological properties and some inclusion relations between these spaces.     

Two-dimension-like functions defined on the class of all Tychonoff spaces

Two-dimension-like functions are constructed on the class of all Tychonoff spaces. Several of their properties, analogous to those of the classical dimension functions, are established.     

Some new generalized difference sequence spaces defined by a sequence of moduli

The idea of difference sequence sets X( ) = {x = (x k ) : x ∈ X} with X = l ∞ , c and c 0 was introduced by Kizmaz [12]. In this paper, using a sequence of moduli we define some generalized difference sequence spaces and give some inclusion relations.     

Estimates for functions in Sobolev spaces defined on unbounded domains

Given a function u belonging to a suitable Beppo–Levi or Sobolev space and an unbounded domain Ω in , we prove several Sobolev-type bounds involving the values of u on an infinite discrete subset A of Ω. These results improve the previous ones obtained by Madych and Potter [W.R. Madych, E.H. Potter, An estimate for multivariate interpolation, J. Approx. Theory 43 (1985) 132–139] and Madych [W.R. Madych, An estimate for multivariate interpolation II, J. Approx. Theory 142 (2006) 116–128].     

Hardy spaces and partial derivatives of conjugate harmonic functions

In this paper we give necessary and sufficient conditions for a harmonic vector and all its partial derivatives to belong to for all .

     

On some new generalized difference sequence spaces defined by a sequence of moduli

In this paper, we define the new generalized difference sequence spaces [V, λ, F, p, q]₀(Δ _v ^m ), [V, λ, F, p, q]₁(Δ _v ^m ) and [V, λ, F, p, q]_∞(Δ _v ^m ). We also study some inclusion relations between these spaces.     

Sequence spaces of fuzzy real numbers defined by Orlicz functions

In this article we study different properties of convergent, null and bounded sequence spaces of fuzzy real numbers defined by an Orlicz function, like completeness, solidness, symmetricity, convergence free etc. We prove some inclusion results, too. The work of the first author was carried under University Grants Commission of India project No.-F. No. 30-240/2004 (RS).     

Generalized continuous functions defined by generalized open sets on generalized topological spaces

We introduce generalized continuous functions defined by generalized open (= g-α-open, g-semi-open, g-preopen, g-β-open) sets in generalized topological spaces which are generalized (g, g′)-continuous functions. We investigate characterizations and relationships among such functions.     

Hilbert scales and Sobolev spaces defined by associated Legendre functions

In this paper we study the Hilbert scales defined by the associated Legendre functions for arbitrary integer values of the parameter. This problem is equivalent to studying the left-definite spectral theory associated to the modified Legendre equation. We give several characterizations of the spaces as weighted Sobolev spaces and prove identities among the spaces corresponding to the lower regularity index.     

On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces

Let $X$ and $ Z$ be Banach spaces, $A$ a closed subset of $X$ and a mapping $f:A\rightarrow Z$ . We give necessary and sufficient conditions to obtain a $C^1$ smooth mapping $F:X \rightarrow Z$ such that $F_{\mid _A}=f$ , when either (i) $X$ and $Z$ are Hilbert spaces and $X$ is separable, or (ii) $X^*$ is separable and $Z$ is an absolute Lipschitz retract, or (iii) $X=L_2$ and $Z=L_p$ with $1<p<2$ , or (iv) $X=L_p$ and $Z=L_2$ with $2<p<\infty $ , where $L_p$ is any separable Banach space $L_p(S,\Sigma ,\mu )$ with $(S,\Sigma ,\mu )$ a $\sigma $ -finite measure space.     

On extensions of Sobolev functions defined on regular subsets of metric measure spaces

We characterize the restrictions of first-order Sobolev functions to regular subsets of a homogeneous metric space and prove the existence of the corresponding linear extension operator.     

Variational functionals defined on spaces ofBV functions and their dependence on boundary data

Summary We extend in a suitable way a class of functionals defined on W ^1,1 (Ω) to the space BV_b(Ω) ⊗ (C(∂Ω))*. Optimization theorems for the extended functional are given. As an application we obtain a known result about minimal surface problems. Entrata in Redazione il 18 luglio 1978. This work was supported in part by Laboratorio per la Matematica Applicata del C.N.R., Italy.