Results 11 to 20 of about 964 (198)
Strong unicity versus modulus of convexity [PDF]
Bulletin of the Australian Mathematical Society, 1994 We show that a Banach space has modulus of convexity of power type p if and only if best approximants to points from straight lines are uniformly strongly unique of order p. Assuming that the space is smooth, we derive a characterisation of the best simultaneous approximant to two elements, and use the characterisation to prove that p–type modulus of ...
Huotari, Robert, Sahab, Salem
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Some properties of Gurarii's modulus of convexity [PDF]
Archiv der Mathematik, 1998 Let \(E\) be a normed linear space, \(S_E\) and \(B_E\) be the unit sphere and unit ball of \(E\), respectively. In the present paper the authors study properties of \textit{V. I. Gurarii's} modulus of convexity [Mat. Issled. 2, No. 1(3), 141-148 (1967; Zbl 0232.46024)] defined by the formula for \(0\leq\varepsilon\leq 2\), \[ \beta_E(\varepsilon ...
Sánchez, Luisa, Ullán, Antonio
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Modulus of convexity for operator convex functions [PDF]
Journal of Mathematical Physics, 2014 Given an operator convex function f(x), we obtain an operator-valued lower bound for cf(x) + (1 − c)f(y) − f(cx + (1 − c)y), c ∈ [0, 1]. The lower bound is expressed in terms of the matrix Bregman divergence. A similar inequality is shown to be false for functions that are convex but not operator convex.
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Modulus of convexity, characteristic of convexity and fixed point theorems [PDF]
Kodai Mathematical Journal, 1987 Various numerical parameters have been introduced to describe the geometric structure of a Banach space E; classical examples are the modulus of convexity \(\delta\) (E;\(\epsilon)\), the characteristic of convexity \(\epsilon_ 0(E)\), and the normal structure coefficient N(E). For instance, if \(\epsilon_ 0(E)=0\) \([\epsilon_ 0(E)
Ishihara, Hajime, Takahashi, Wataru
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Weakly convex sets and modulus of nonconvexity
Journal of Mathematical Analysis and Applications, 2010 We consider a definition of a weakly convex set which is a generalization of the notion of a weakly convex set in the sense of Vial and a proximally smooth set in the sense of Clarke, from the case of the Hilbert space to a class of Banach spaces with the modulus of convexity of the second order.
Balashov, Maxim V. +1 more
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On the modulus of U‐convexity [PDF]
Abstract and Applied Analysis, 2005 We prove that the moduli of U‐convexity, introduced by Gao (1995), of the ultrapower of a Banach space X and of X itself coincide whenever X is super‐reflexive. As a consequence, some known results have been proved and improved. More precisely, we prove that uX(1) > 0 implies that both X and the dual space X∗ of X have uniform normal structure and ...
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Analog of modulus of convexity for Grand Lebesgue Spaces
, 2021 We introduce and evaluate the degree of convexity of an unit ball, so-called, characteristic of convexity (COC) for the Grand Lebesgue Spaces, (GLS), which is a slight analog of the classical notion of the modulus of convexity (MOC).
Formica, M. R. +2 more
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A note on the modulus of convexity [PDF]
Glasgow Mathematical Journal, 1981 In [1, Corollary 5], Figiel gives an elegant demonstration that the modulus ofconvexity δ in real Banach space X is nondecreasing, whereIt is deduced from this that in fact δ(ɛ)/ɛ is nondecreasing [Proposition 3]. During the course of the proof [Lemma 4] it is stated that if v ∊ Sx is a local maximum on Sx of φ ∈Sx*, then v is a global maximum (φ(v ...
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Uniformly convex subsets of the Hilbert space with modulus of convexity of the second order
Journal of Mathematical Analysis and Applications, 2011 We prove that in the Hilbert space every uniformly convex set with modulus of convexity of the second order at zero is an intersection of closed balls of fixed radius. We also obtain an estimate of this radius.
Balashov, Maxim V. +1 more
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Modulus of convexity in Banach spaces
Applied Mathematics Letters, 2003 It is well-known [\textit{K. Goebel}, Compos. Math. 22, 269--274 (1970; Zbl 0202.12802)] that if the modulus of convexity \(\delta_X(\varepsilon)\) of a Banach space \(X\) satisfies \(\delta_X(1)>0\), then \(X\) has uniform normal structure. Less well-known is the result of the author and \textit{K. S. Lau} [Stud. Math. 99, 41--56 (1991; Zbl 0757.46023)
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