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1
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On starlikeness of certain integral transforms

100%
Ponnusamy S.
Annales Polonici Mathematici
|
1991-1992
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tom 56
|
nr 3
227-232
EN
Let A denote the class of normalized analytic functions in the unit disc U = {z: |z| < 1}. The author obtains fixed values of δ and ϱ (δ ≈ 0.308390864..., ϱ ≈ 0.0903572...) such that the integral transforms F and G defined by $F(z) = ∫_0^z (f(t)/t)dt$ and $G(z) = (2/z) ∫_0^z g(t)dt$ are starlike (univalent) in U, whenever f ∈ A and g ∈ A satisfy Ref'(z) > -δ and Re g'(z) > -ϱ respectively in U.
2
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Attenuating the singularities of plurisubharmonic functions

100%
Kiselman C.
Annales Polonici Mathematici
|
1994-1995
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tom 60
|
nr 2
173-197
EO
Resumo (Malfortigi la malregulejojn la plursubharmonaj funkcioj). Ni studas la malregulejojn de la plursubharmonaj funkcioj per metodoj de la konveksa analitiko. Teoremoj pri analitikeco de rafinita nombro de Lelong estas pruvitaj.
EN
We study the singularities of plurisubharmonic functions using methods from convexity theory. Analyticity theorems for a refined Lelong number are proved.
3
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Analytic and $C^k$ approximations of norms in separable Banach spaces

100%
Deville R., Fonf V., Hájek P.
Studia Mathematica
|
1996
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tom 120
|
nr 1
61-74
EN
We prove that in separable Hilbert spaces, in $ℓ_{p}(ℕ)$ for p an even integer, and in $L_{p}[0,1]$ for p an even integer, every equivalent norm can be approximated uniformly on bounded sets by analytic norms. In $ℓ_{p}(ℕ)$ and in $L_{p}[0,1]$ for p ∉ ℕ (resp. for p an odd integer), every equivalent norm can be approximated uniformly on bounded sets by $C^[p]}$-smooth norms (resp. by $C^{p-1}$-smooth norms).
4
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Operator inequalities of Jensen type

100%
Moslehian M. S., Mićić J., Kian M.
Topological Algebra and its Applications
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2013
|
tom 1
9-21
EN
We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators. Among other things, we prove that if f : [0;1) → ℝ is a continuous convex function with f(0) ≤ 0, then [...] for all operators Ci such that [...] (i=1 , ... , n) for some scalar M ≥ 0, where [...] and [...]
5
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Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities

75%
Matkowski J., Świątkowski T.
Fundamenta Mathematicae
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1993
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tom 143
|
nr 1
75-85
EN
Let ϕ be an arbitrary bijection of $ℝ_+$. We prove that if the two-place function $ϕ^{-1}[ϕ (s)+ϕ (t)]$ is subadditive in $ℝ^2_+$ then $ϕ $ must be a convex homeomorphism of $ℝ_+$. This is a partial converse of Mulholland's inequality. Some new properties of subadditive bijections of $ℝ_+$ are also given. We apply the above results to obtain several converses of Minkowski's inequality.
6
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Weak nearly uniform smoothness of the \(\psi\)-direct sums \((X_1 \oplus \dots\oplus X_N)_\psi\)

75%
Kato M., Tamura T.
Commentationes Mathematicae
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2012
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tom 52
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nr 2
EN
We shall characterize the weak nearly uniform smoothness of the \(\psi\)-direct sum \((X_1\oplus \dots\oplus X_N)_\psi\) of \(N\) Banach spaces \(X_1,\dots,X_N\), where \(\psi\) is a convex function satisfying certain conditions on the convex set \(\Delta_N = \{(s_1 ,\dots , s_{N-1})\in \mathbb{R}_+^{N-1} : \sum_{i=1}^{N-1} s_i \leq 1\). To do this a class of convex functions which yield \(\ell_1\)-like norms will be introduced. We shall apply our result to the fixed point property for nonexpansive mappings (FPP). In particular an example will be presented which indicates that there are plenty of Banach spaces with FPP failing to be uniformly non-square.
7
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The converse of the Hölder inequality and its generalizations

75%
Matkowski J.
Studia Mathematica
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1994
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tom 109
|
nr 2
171-182
EN
Let (Ω,Σ,μ) be a measure space with two sets A,B ∈ Σ such that 0 < μ (A) < 1 < μ (B) < ∞ and suppose that ϕ and ψ are arbitrary bijections of [0,∞) such that ϕ(0) = ψ(0) = 0. The main result says that if $ʃ_Ω xydμ ≤ ϕ^{-1} (ʃ_{Ω} ϕ∘x dμ) ψ^{-1} (ʃ_{Ω} ψ∘x dμ)$ for all μ-integrable nonnegative step functions x,y then ϕ and ψ must be conjugate power functions. If the measure space (Ω,Σ,μ) has one of the following properties: (a) μ (A) ≤ 1 for every A ∈ Σ of finite measure; (b) μ (A) ≥ 1 for every A ∈ Σ of positive measure, then there exist some broad classes of nonpower bijections ϕ and ψ such that the above inequality holds true. A general inequality which contains integral Hölder and Minkowski inequalities as very special cases is also given.
8
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Weak nearly uniform soothness and worth property of \(\psi\)-direct sums of Banach spaces

63%
Kato M., Tamura T.
Commentationes Mathematicae
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2006
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tom 46
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nr 1
EN
We shall characterize the weak nearly uniform smoothness of the \(\psi\)-direct sum \(X \oplus_\psi Y\) of Banach spaces \(X\) and \(Y\). The Schur and WORTH properties will be also characterized. As a consequence we shall see in the \(\ell_\infty\)-sums of Banach spaces there are many examples of Banach spaces with the fixed point property which are not uniformly non-square.
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