Results 291 to 300 of about 173,242 (326)

The Alternating Algorithm in Uniformly Convex Spaces

Journal of the London Mathematical Society, 1984
Let X be a real Banach space and let U,V be two proximinal subspaces of X with proximinal maps \(P_ u,P_ v\) respectively. The sequence \(\{K^ n\}\), where \(K=(I-P_ v)(I-P_ U)\), defines the alternating algorithm. The space X is said to admit the alternating algorithm if for every triple (x,U,V) \(K^ nx\) converges to a point of the form x-w, where w ...
C. Franchetti, Will Light
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BASES IN UNIFORMLY CONVEX AND UNIFORMLY FLATTENED BANACH SPACES

Mathematics of the USSR-Izvestiya, 1971
The aim of this article is to obtain two-sided estimates for the norm of an element x in a uniformly convex and uniformly flattened Banach space E in terms of lp-norms of the sequence of coefficients which occur in the expansion of x in a basis .
V I Gurariĭ, N I Gurariĭ
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Uniformly smooth renormings of uniformly convex Banach spaces

Journal of Soviet Mathematics, 1985
Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 135, 120-134 (Russian) (1984; Zbl 0538.46014).
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Martingales with values in uniformly convex spaces

Israel Journal of Mathematics, 1975
Using the techniques of martingale inequalities in the case of Banach space valued martingales, we give a new proof of a theorem of Enflo: every super-reflexive space admits an equivalent uniformly convex norm. Letr be a number in ]2, ∞[; we prove moreover that if a Banach spaceX is uniformly convex (resp.
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On nearly uniformly convex Banach spaces

Mathematical Proceedings of the Cambridge Philosophical Society, 1983
A real Banach space (X, ‖ · ‖) is said to be uniformly convex (UC) (or uniformly rotund) if for all ∈ > 0 there is a δ > 0 such that if ‖x| ≤ 1, ‖y‖ ≤ 1 and ‖x−y‖ ≥ ∈, then ‖(x + y)/2‖ ≤ 1− δ.
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A note on k-uniformly convex spaces

Mathematical Proceedings of the Cambridge Philosophical Society, 1985
AbstractIn this short note we prove that Istrǎƫescu's notion of k-uniform (k-locally uniform) convexity of a Banach space is actually equivalent to the notion of uniform (locally uniform) convexity. Thus theorem 2 in [3] and theorem 2·6·28 in [2] are trivially true.
Sung Kyu Choi, Jong Sook Bae
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Uniformly convex Banach spaces are reflexive—constructively [PDF]

Mathematical Logic Quarterly, 2013
We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the Milman‐Pettis theorem that uniformly convex Banach spaces are reflexive.
Douglas S. Bridges, Hajime Ishihara, Maarten McKubre-Jordens   +2 more
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Hadamard–Landau inequalities in uniformly convex spaces

Mathematical Proceedings of the Cambridge Philosophical Society, 1981
The inequalityfor fεLp(− ∞, ∞)or Lp(0, ∞) (1≤p ≤ ∞), and its extensionfor T an Hermitian or dissipative linear operator, in general unbounded, on a Banach space X, for xεX, have been considered by many authors. In particular, forms of inequality (1) have been given by Hadamard(7), Landau(15), and Hardy and Little-wood(8),(9).
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On embedding trees into uniformly convex Banach spaces

Israel Journal of Mathematics, 1999
The author deals with an investigation into the minimum value of \(D= D(n)\) such that any \(n\)-point tree metric space \((T,\rho)\) can be \(D\)-embedded into a given Banach space \((X,\|\cdot\|)\); i.e., there exists a mapping \(f: T\to X\) such that \(D^{-1}\rho(x,y)\leq\|f(x)- f(y)\|\leq \rho(x,y)\) for all \(x,y\in T\). Bourgain showed that \(X\)
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MARTINGALE REPRESENTATION IN NEARLY UNIFORMLY CONVEX SPACES

Acta Mathematica Scientia, 1995
Summary: We give a martingale representation in nearly uniformly convex Banach spaces. Our result generalizes the representation theorem established by \textit{D. Landers} and \textit{L. Rogge} [Proc. Am. Math. Soc. 75, No. 1, 108-110 (1979; Zbl 0403.60046)].
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