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1
Content available remote On Uniform Differentiability
100%
Rolewicz S.
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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.
2
Content available remote On the Rockafellar theorem for $Φ^{γ(·,·)}$-monotone multifunctions
100%
Rolewicz S.
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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, $Γ(x) ⊂ ∂_{Φ}^{γ(·,·)} f|_{x}$.
3
Content available remote An extension of Mazur's theorem on Gateaux differentiability to the class of strongly α (·)-paraconvex functions
100%
Rolewicz S.
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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 $A_{G}$.
4
Content available remote On differentiability of strongly α(·)-paraconvex functions in non-separable Asplund spaces
100%
Rolewicz S.
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tom 167
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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.
5
Content available remote On smooth points of boundaries of open sets
100%
Rolewicz S.
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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.
6
Content available remote On automatic boundedness of Nemytskiĭ set-valued operators
63%
Rolewicz S. , Song W.
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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 $sup{ϱ_{M,μ}(y): y ∈ N_F(K)} < ∞$.
7
Content available Remarks on \(\phi\)-operators in linear topological spaces
63%
Przeworska-Rolewicz D. , Rolewicz S.
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tom 9
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nr 1
EN
The article contains no abstract
8
Content available On d-characteristic and $d_Ξ$-characteristic of linear operators
51%
Przeworska-Rolewicz D. , Rolewicz S.
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1967
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tom 19
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nr 2
117-121
9
Content available remote On integrals of functions with values in a complete linear metric spaces
51%
Przeworska-Rolewicz D. , Rolewicz S.
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tom 26
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nr 2
121-131
10
Content available remote On perturbations of deviations of periodic differential-difference equations in Banach spaces
50%
Rolewicz S.
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tom 47
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nr 1
31-35
11
Content available remote On operators preserving a conjugate space
38%
Przeworska-Rolewicz D. , Rolewicz S.
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nr 2
245-249
12
Content available remote Remarks on the existence of the Riemann-Stieltjes integral
38%
Pełczyński A. , Rolewicz S.
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tom 5
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nr 1
74-77
13
Content available remote On the control of linear periodic time lag systems
38%
Przeworska-Rolewicz D. , Rolewicz S.
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nr 2
149-152
14
Content available remote An example of a normal space non-isomorphic to its product by the real line
38%
Rolewicz S.
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nr 1
71-75
15
Content available remote Sufficient condition for Pareto optimization in Banach spaces
38%
Rolewicz S.
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nr 2
111-114
16
Content available remote Entire functions in $B_{0}$-algebras containing dense division algebras
38%
Rolewicz S.
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tom 23
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nr 2
181-187
17
Content available remote On the minimum time control problem and continuous families of convex sets
38%
Rolewicz S.
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tom 56
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nr 1
39-45
18
Content available Concerning the characterization of linear spaces
32%
Hartman S. , Mycielski J. , Rolewicz S. , Schinzel A.
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tom 13
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nr 2
199-208
19
Content available remote Some properties of the norm in F-spaces
32%
Bessaga C. , Pełczyński A. , Rolewicz S.
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tom 16
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nr 2
183-192
20
Content available On unconditional convergence in linear metric spaces
32%
Rolewicz S. , Ryll-Nardzewski C.
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tom 17
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nr 2
327-331
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