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1
Content available remote

On differentiability of strongly α(·)-paraconvex functions in non-separable Asplund spaces

100%
Rolewicz S.
Studia Mathematica
|
2005
|
tom 167
|
nr 3
235-244
EN
In Rolewicz (2002) it was proved that every strongly α(·)-paraconvex function defined on an open convex set in a separable Asplund space is Fréchet differentiable on a residual set. In this paper it is shown that the assumption of separability is not essential.
2
Content available remote

On α(·)-monotone multifunctions and differentiability of γ-paraconvex functions

100%
Rolewicz S.
Studia Mathematica
|
1999
|
tom 133
|
nr 1
29-37
EN
Let (X,d) be a metric space. Let Φ be a family of real-valued functions defined on X. Sufficient conditions are given for an α(·)-monotone multifunction $Γ: X → 2^Φ$ to be single-valued and continuous on a weakly angle-small set. As an application it is shown that a γ-paraconvex function defined on an open convex subset of a Banach space having separable dual is Fréchet differentiable on a residual set.
3
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On the Rockafellar theorem for $Φ^{γ(·,·)}$-monotone multifunctions

100%
Rolewicz S.
Studia Mathematica
|
2006
|
tom 172
|
nr 2
197-202
EN
Let X be an arbitrary set, and γ: X × X → ℝ any function. Let Φ be a family of real-valued functions defined on X. Let $Γ: X → 2^{Φ}$ be a cyclic $Φ^{γ(·,·)}$-monotone multifunction with non-empty values. It is shown that the following generalization of the Rockafellar theorem holds. There is a function f: X → ℝ such that Γ is contained in the $Φ^{γ(·,·)}$-subdifferential of f, $Γ(x) ⊂ ∂_{Φ}^{γ(·,·)} f|_{x}$.
4
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An extension of Mazur's theorem on Gateaux differentiability to the class of strongly α (·)-paraconvex functions

100%
Rolewicz S.
Studia Mathematica
|
2006
|
tom 172
|
nr 3
243-248
EN
Let (X,||·||) be a separable real Banach space. Let f be a real-valued strongly α(·)-paraconvex function defined on an open convex subset Ω ⊂ X, i.e. such that $f(tx + (1-t)y) ≤ tf(x) + (1-t)f(y) + min[t,(1-t)]α(||x-y||)$. Then there is a dense $G_{δ}$-set $A_{G} ⊂ Ω$ such that f is Gateaux differentiable at every point of $A_{G}$.
5
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Uwaga o wahaniu Kronroda funkcji dwóch zmiennych

100%
Rolewicz S.
Commentationes Mathematicae
|
1959
|
tom 3
|
nr 1
EN
The article contains no abstract
6
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O domkniętości rzutu podprzestrzeni w przestrzeniach Banacha

100%
Rolewicz S.
Commentationes Mathematicae
|
1959
|
tom 3
|
nr 1
EN
The article contains no abstract
7
Content available remote

On smooth points of boundaries of open sets

100%
Rolewicz S.
Studia Mathematica
|
2009
|
tom 191
|
nr 3
211-214
EN
The notions of smooth points of the boundary of an open set and α(·) intrinsically paraconvex sets are introduced. It is shown that for an α(·) intrinsically paraconvex open set the set of smooth points is a dense $G_{δ}$-set of the boundary.
8
Content available remote

On Uniform Differentiability

100%
Rolewicz S.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2008
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tom 56
|
nr 3
231-237
EN
We introduce the notion of uniform Fréchet differentiability of mappings between Banach spaces, and we give some sufficient conditions for this property to hold.
9
Content available remote

On $𝚽^{γ(·,·)}$-subdifferentiable and [𝚽+γ]-subdifferentiable Functions

100%
Rolewicz S.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2005
|
tom 53
|
nr 3
273-279
EN
Let X be an arbitrary set. Let 𝚽 be a family of real-valued functions defined on X. Let γ:X × X → ℝ. Set [𝚽 + γ] = {Φ(·) + γ(·,x) | Φ ∈ 𝚽, x ∈ X}$. We give conditions guaranteeing the equivalence of $𝚽^{γ(·,·)}$-subdifferentiability and [𝚽 + γ]-subdifferentiability.
10
Content available remote

On cyclic α(·)-monotone multifunctions

100%
Rolewicz S.
Studia Mathematica
|
2000
|
tom 141
|
nr 3
263-272
EN
Let (X,d) be a metric space. Let Φ be a linear family of real-valued functions defined on X. Let $Γ: X → 2^{Φ}$ be a maximal cyclic α(·)-monotone multifunction with non-empty values. We give a sufficient condition on α(·) and Φ for the following generalization of the Rockafellar theorem to hold. There is a function f on X, weakly Φ-convex with modulus α(·), such that Γ is the weak Φ-subdifferential of f with modulus α(·), $Γ(x)=∂^{-α}_{Φ}f|_{x}$.
11
Content available remote

On multi-dimensional generalizations of the Wiener-Żelazko and Lévy-Żelazko theorems

100%
Rolewicz S.
Banach Center Publications
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2005
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tom 67
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nr 1
283-291
EN
Multi-dimensional generalizations of the Wiener-Żelazko and Lévy-Żelazko theorems are obtained.
12
Content available remote

On locally bounded algebras

100%
Rolewicz S.
Banach Center Publications
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2000
|
tom 53
|
nr 1
191-198
EN
It is a survey talk concerning locally bounded algebras.
13
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Remarks on \(\phi\)-operators in linear topological spaces

64%
Przeworska-Rolewicz D., Rolewicz S.
Commentationes Mathematicae
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1965
|
tom 9
|
nr 1
EN
The article contains no abstract
14
Content available remote

Local completeness of locally pseudoconvex spaces and Borwein-Preiss variational principle

64%
Qiu J., Rolewicz S.
Studia Mathematica
|
2007
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tom 183
|
nr 2
99-115
EN
The notion of local completeness is extended to locally pseudoconvex spaces. Then a general version of the Borwein-Preiss variational principle in locally complete locally pseudoconvex spaces is given, where the perturbation is an infinite sum involving differentiable real-valued functions and subadditive functionals. From this, some particular versions of the Borwein-Preiss variational principle are derived. In particular, a version with respect to the Minkowski gauge of a bounded closed convex set in a locally convex space is presented. In locally convex spaces it can be shown that the relevant perturbation only consists of a single summand if and only if the bounded closed convex set has the quasi-weak drop property if and only if it is weakly compact. From this, a new description of reflexive locally convex spaces is obtained.
15
Content available remote

Ekeland's variational principle in locally p-convex spaces and related results

64%
Qiu J., Rolewicz S.
Studia Mathematica
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2008
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tom 186
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nr 3
219-235
EN
In the framework of locally p-convex spaces, two versions of Ekeland's variational principle and two versions of Caristi's fixed point theorem are given. It is shown that the four results are mutually equivalent. Moreover, by using the local completeness theory, a p-drop theorem in locally p-convex spaces is proven.
16
Content available remote

On automatic boundedness of Nemytskiĭ set-valued operators

64%
Rolewicz S., Song W.
Studia Mathematica
|
1995
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tom 113
|
nr 1
65-72
EN
Let X, Y be two separable F-spaces. Let (Ω,Σ,μ) be a measure space with μ complete, non-atomic and σ-finite. Let $N_F$ be the Nemytskiĭ set-valued operator induced by a sup-measurable set-valued function $F:Ω × X → 2^{Y}$. It is shown that if $N_F$ maps a modular space $(N(L(Ω,Σ,μ;X)), ϱ_{N,μ})$ into subsets of a modular space $(M(L(Ω,Σ,μ;Y)),ϱ_{M,μ})$, then $N_F$ is automatically modular bounded, i.e. for each set K ⊂ N(L(Ω,Σ,μ;X)) such that $r_K = sup{ϱ_{N,μ}(x) : x ∈ K} < ∞$ we have $sup{ϱ_{M,μ}(y): y ∈ N_F(K)} < ∞$.
17
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

The only continuous Volterra right inverses in $C_c[0,1]$ of the operator $d/dt$ are $ʃ^t_a$

64%
Przeworska-Rolewicz D., Rolewicz S.
Colloquium Mathematicum
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1987
|
tom 51
|
nr 1
281-285
18
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

A method of reduction of constraints

63%
Rolewicz S.
Banach Center Publications
|
1985
|
tom 14
|
nr 1
469-476
19
Content available remote

Approximative dimension of linear topological spaces and some of its applications

52%
Bessaga C., Pełczyński A., Rolewicz S.
Studia Mathematica
|
1963
|
tom Special Series
|
nr 1
27-29
20
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

On d-characteristic and $d_Ξ$-characteristic of linear operators

51%
Przeworska-Rolewicz D., Rolewicz S.
Annales Polonici Mathematici
|
1967
|
tom 19
|
nr 2
117-121
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