Language:
EN
| Published:
30-09-1992
|
Abstract
| pp. 21-29
Let lϕ be a Musielak-Orlicz sequence space. Let X1ϕ and Xϕ be the modular spaces of multifunctions generated by lϕ. Let Kw,j: R→R for j = 0,1,2,..., w∈W, where W is an abstract set of indices. Assuming certain singularity assumption on the nonlinear kernel Kw,j and setting Tw(F)=(Tw(F)(i))i=0∞ with (Tw(F))(i) = {Σj=0iKw,j(f(j)) : f(j)∈F(j)}, convergence theorems Tw(F)→ϕ F in X1ϕ and Tw(F)→d,ϕ, F in Xϕ are obtained.
Language:
EN
| Published:
28-08-2023
|
Abstract
| pp. 240-247
In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma generalizes some results for a class of Orlicz-Sobolev spaces. What matters here is the behavior of the integral, not the space.
Language:
EN
| Published:
22-03-2022
|
Abstract
| pp. 15-25
This paper presents a constructive proof of the existence of a regular non-atomic strictly-positive measure on any second-countable non-atomic locally compact Hausdorff space. This construction involves a sequence of finitely-additive set functions defined recursively on an ascending sequence of rings of subsets with a set function limit that is extendable to a measure with the desired properties. Non-atomicity of the space provides a meticulous way to ensure that the set function limit is σ-additive.
Language:
EN
| Published:
08-01-2025
|
Abstract
| pp. 248-268
The sequence spaces ruℓ∞(O, ∇q), ruℓp(O, ∇q), ruc(O, ∇q), ruc0(O, ∇q), rumφ(O, ∇q, p), runφ(O, ∇q, p), rumφ(O, ∇q), runφ(O, ∇q) are defined by the Orlicz function in this article. We examine all of its characteristics, including symmetry, solidity, and completeness. A few geometric properties on convexity on the space rumφ(O, ∇q, p) are also examined in this article.
Language:
EN
| Published:
30-01-2003
|
Abstract
| pp. 7-16
The object of this paper is to obtain necessary and sufficient conditions to characterize the matrices in classes (l∞y(p,s),l∞(q)), (c0y(p,s),l∞(q)),(l∞y(p,s),c0(q)), and(c0y(p,s),c0(q)) which will fill up a gap in the existing literature.
Language:
EN
| Published:
30-09-2005
|
Abstract
| pp. 23-29
Two dual sequence functions describing some kind of local convexity and dimension of subspaces of linear metric spaces are introduced. It is shown that the functions give a useful tool in the investigations of fixed point properties of the Schauder type.
2005-09-30
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English