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1
Content available remote Density of smooth functions in Sobolev spaces "wth mixed functions"
Liskowski M.
Fasciculi Mathematici
|
2014
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Nr 53
77--83
EN
The results presented in this paper concern approximation by smooth functions in the Sobolev spaces defined by means of a modular (1). These spaces can be a natural medium to study the partial differential equations with rapidly or slowly increasing coefficients (i.e. the coefficients are of a nonpolynomial type).
2
Content available remote Sobolev spaces "with mixed functions"
Liskowski M.
Fasciculi Mathematici
|
2012
|
Nr 48
73--82
EN
This paper describes some generalization of modular function spaces Lϕψ defined by a modular Iϕѱ(f) = ∫baϕ (x, ∫dc ψ (y, f (x,y))dy) dx, ([3]). The next part of this paper focuses on using of spaces, defined previously, to introduce Sobolev spaces as a vector subspace of the generalized space Lϕѱ. Some selected properties of these spaces are presented.
3
Content available remote On the Existence of Common Fixed Points for Semigroups of Nonlinear Mappings in Modular Function Spaces
Kozłowski W. M.
Commentationes Mathematicae
|
2011
|
Vol. 51, [Z] 1
81-98
EN
Let C be a ρ-bounded, ρ -closed, convex subset of a modular function space Lρ. We investigate the existence of common fixed points for semigroups of nonlinear mappings Tt : C → C, i.e. a family such that T0(x) = x, Ts+t = Ts(Tt(x)), where each Tt is either ρ -contraction or ρ -nonexpansive. We also briefly discuss existence of such semigroups and touch upon applications to differential equations.
4
Content available remote An approximation theorem in Musielak-Orlicz-Sobolev spaces
Benkirane A., Douieb J., Ould Mohamedhen Val M.
Commentationes Mathematicae
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2011
|
Vol. 51, [Z] 1
109-120
EN
In this paper we prove the uniform boundedness of the operators of convolution in the Musielak-Orlicz spaces and the density of C[...]in the Musielak-Orlicz-Sobolev spaces by assuming a condition of Log-Hölder type of continuity.
5
Content available remote On the generalized Nakano sequence space
Sengonul M.
Demonstratio Mathematica
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2007
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Vol. 40, nr 4
885-893
EN
The purpose of this note is to define and to investigate the generalized Nakano sequence space A(p) and to show that the sequence space A(p) eąuipped with the Luxemburg norm is rotund and posses property-H when p = (pk) is bounded with pk > 1 for all k is an element of N.
6
Content available remote Korovkin theorem in modular spaces
Bardaro C., Mantellini I.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2007
|
Vol. 47, [Z] 2
239-253
EN
In this paper we obtain an extension of the classical Korovkin theorem in abstract modular spaces. Applications to some discrete and integral operators are discussed.
7
Content available remote An application of modular spaces to approximation problems, IX
Stoiński S.
Fasciculi Mathematici
|
2002
|
Nr 33
89-97
EN
By means of terms of a sequence (pn), where pn, n = l,2,..., are pseudomodulars, and by means of an infinite matrix A = [amn ] of non-negative numbers we shall construct the modular spaces XpAos' and Xp^os. Then we shall approximate elements of these spaces by means of terms of a sequence (p.), where p, i = l,2,..., are pseudomodulars. In particular, we will investigate the special cases when pn and pt are singular integrals.
8
Content available remote On nonlinear integral equations in some functions spaces
Bardaro C., Musielak J., Vinti G.
Demonstratio Mathematica
|
2002
|
Vol. 35, nr 3
583-592
EN
There are established some conditions for existence of solutions of a nonlinear integral equation Tf =f+g, where T is a convolution-type integral operator.
9
Content available remote Integral of function with values in complete modular space
Liskowski M.
Demonstratio Mathematica
|
2002
|
Vol. 35, nr 2
347-356
EN
The theorem on existence of an integral of a function with values in a modular space and some fundamental properties of this integral are given.
10
Content available remote An application of modular spaces to approximation problems, VII
Stoiński S.
Demonstratio Mathematica
|
2000
|
Vol. 33, nr 4
805-814
11
Content available remote The Musielak-Orlicz relations between some modular spaces
Waszak A., Żurakowski D.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2000
|
[Z] 40
225-234
EN
Let T be the space of all real double sequences. For a given matrix A and fi-function f we consider two modular spaces connected with strong (A,fi) and | A,fi| summability. This paper contains some generalization of theorems given by J.Musielak and W.Orlicz in [4] and [5].
12
Content available remote Interpolation inequalities in Orlicz-Sobolev space
Liskowski M.
Fasciculi Mathematici
|
1999
|
Nr 30
99-106
EN
We consider the problem of detennining upper bounds for nonns of functions from Orlicz-Sobolev space[...], [...] in tenns of nonns of the space [...] and Orlicz space. The interpolation inequalities of this type are well-known for classical Sobolev spaces [...], [...]and also [1].
13
Content available remote Approximation with respect to a measure in a modular space, VI
Stoiński S.
Fasciculi Mathematici
|
1999
|
Nr 29
125-131
EN
Elements of a modular subspace of [...] are approximated by certain singular integrals.
14
Content available remote On consistency of summability methods generated by nonlinear integral operators
Tomasz B.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
1999
|
[Z] 39
197-205
EN
Let r,n be two modulars on L(G), and let W be an abstract set of indices. For nonlinear integral op-erators T(w) and S(w) on L(G), we give sufficient conditions for two methods of summability gen-erated by T(w) and S(w) to be consistent for sequences (f(w)) of functions of L(G), in the sense of modular r.
15
Content available remote Approximation by means of certain non-linear operators in some modular spaces
Stoiński S.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
1999
|
[Z] 39
173-180
EN
Elements of certain modular spaces are approximated by certain singular integrals.
16
Content available remote On random Lipschitz condition and its application in approximation theory
Musielak J.
Fasciculi Mathematici
|
1998
|
Nr 28
119-125
EN
There are estimated moduli of continuity of functions satisfying Lipschitz condition with random exponents both in the sense of convergence in probability and convergence in mean. The results are applied to extend Jackson's direct approximation theorem to the case of Lipschitz condition with a random exponent.
17
Content available remote Musielak-Orlicz spaces of sequences connected with strong summability
Waszak A., Żurakowski D.
Fasciculi Mathematici
|
1998
|
Nr 28
157-165
18
Content available remote Generalized sampling operators in modular spaces
Mantellini I.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
1998
|
[Z] 38
77-92
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