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Coarse Embedding Into Uniformly Convex Banach Spaces

Chinese Annals of Mathematics Series B, 2014
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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 .
Gurarij, V. I., Gurarij, N. I.
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Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces

Journal of Convex Analysis, 2000
The aim of the paper is to show that, in uniformly convex Banach spaces, the powers of the norm with exponent r > 1 share a property called total convexity. Using this fact we establish a formula for determining Bregman projections on closed hyperplanes and half spaces.
Butnariu, Dan, Iusem, Alfredo N., Resmerita, Elena   +2 more
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Uniformly Strongly Convex Banach Spaces

Mediterranean Journal of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shunmugaraj, P., Zălinescu, Constantin
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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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A Universal Reflexive Space for the Class of Uniformly Convex Banach Spaces [PDF]

Mathematische Annalen, 2006
We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J. Bourgain. We also give intrinsic characterizations of separable reflexive Banach spaces which embed into a reflexive space with a block $q$-Hilbertian and/or a block $p$-Besselian ...
Thomas Schlumprecht, E Odell
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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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Nonexpansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces

Georgian Mathematical Journal, 2002
Abstract 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.
Yeol Je Cho, Ravi Agarwal, Haiyun Zhou
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Uniformly Convex Sets in Banach Spaces

Mathematical Notes
For a normed space \(X\) and for two equivalent asymmetric norms \(\mu_U\), \(\mu_V\) on \(X\) generated by asymmetric unit balls \(U\) and \(V\) respectively, the author introduces and studies the following modulus of convexity of a set \(C \subset X\): \[ \delta_{C,U,V}(\varepsilon)=\inf\left\{\mu_U\left(z-\frac{x+y}{2}\right): x,y \in C, z \in X ...
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Farthest points of sets in uniformly convex banach spaces

Israel Journal of Mathematics, 1966
LetS 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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