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An estimate for the type of a complexly uniformly convex Banach space [PDF]
Mathematical Notes of the Academy of Sciences of the USSR, 1985 Let X be a complex Banach space with the unit sphere S. The modulus of convexity \(\delta\) (t) of X is introduced by \(\delta (t)=\inf \{\max \{\| x+thy\|:h\in H\}:x,y\in S\}-1\), \(t>0\), where \(H=\{1,-1,i,- i\}\). According to \textit{J. Globevnik} [Proc. Am. Math. Soc.
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On embedding trees into uniformly convex Banach spaces
Israel Journal of Mathematics, 1999The 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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Smoothness of the distribution of the norm in uniformly convex Banach spaces
Journal of Theoretical Probability, 1990Let (E, ‖ · ‖) be a uniformly convex Banach space of power type. In this paper we investigate differentiability properties of the distribution function of the norm of a random series with one-dimensional independent components inE.
Michał Ryznar, Tomasz Byczkowski
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Nonexpansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces
gmj, 2002Abstract In this paper, most of classical and modern convergence theorems of iterative schemes for nonexpansive mappings are presented and the main results in the paper generalize and improve the corresponding results given by many authors.
Ravi P. Agarwal +3 more
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Farthest points of sets in uniformly convex banach spaces
Israel Journal of Mathematics, 1966LetS be a closed and bounded set in a uniformly convex Banach spaceX. It is shown that the set of all points inX which have a farthest point inS is dense. Letb(S) denote the set of all farthest points ofS, then a sufficient condition for $$\overline {co} S = \overline {co} b(S)
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Pointwise Lipschitzian mappings in uniformly convex and uniformly smooth Banach spaces
Nonlinear Analysis: Theory, Methods & Applications, 2013Abstract Let X be a uniformly convex and uniformly smooth Banach space. Let T : C → C be an asymptotic pointwise nonexpansive mapping, where C is a bounded, closed and convex subset of X . In this paper we investigate conditions sufficient for the weak convergence of the generalized Mann and Ishikawa processes to a fixed ...
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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Multifunctional biomolecule nanostructures for cancer therapy
Nature Reviews Materials, 2021Jing Wang, Yiye Li, Guangjun Nie
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Cosmology with the Laser Interferometer Space Antenna
Living Reviews in Relativity, 2023Germano Nardini
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