Results 21 to 30 of about 165,935,923 (285)
Differences of Positive Linear Operators on Simplices
Journal of Function Spaces, 2021 The aim of the paper is twofold: we introduce new positive linear operators acting on continuous functions defined on a simplex and then estimate differences involving them and/or other known operators.
Ana-Maria Acu +2 more
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Discrete $d$-dimensional moduli of smoothness [PDF]
Proceedings of the American Mathematical Society, 2014 We show that on the $d$-dimensional cube $I^d\equiv [0,1]^d$ the discrete moduli of smoothness which use only the values of the function on a diadic mesh are sufficient to determine the moduli of smoothness of that function. As an important special case our result implies for $f\in C(I^d)$ and given integer $r$ that when $0<α0$ and $|u|=1$ such that
Ditzian, Z., Prymak, A.
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Directional Moduli of Rotundity and Smoothness
, 2021 We study various notions of directional moduli of rotundity and when such moduli of rotundity of power type imply the underlying space is superreflexive. Duality with directional moduli of smoothness and some applications are also discussed.
Giles, John R. +2 more
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On Generalized Moduli of Quasi-Banach Space
Journal of Function Spaces, 2018 We shall discuss three generalized moduli such as generalized modulus of convexity, modulus of smoothness, and modulus of Zou-Cui of quasi-Banach spaces and give some important properties of these moduli.
Young Chel Kwun +4 more
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K-moduli, moduli of smoothness, and Bernstein polynomials on a simplex
Indagationes Mathematicae, 1991 Let \(f\in C[0,1]\) and let \(B_ n(f,x)\) be the classical Bernstein polynomials associated to \(f\). The approximation behavior of \(B_ n(f,x)\) is related to the weighted \(K\)-modulus \(K_ \varphi^ 2(f,t)\), for example by \(\| B_ n f-f\|_ \infty \leq C\cdot K_ \varphi^ 2\bigl(f,{1\over{n+1}}\bigr)\). (See, for example, \textit{H.
Berens, H., Xu, Y.
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Directional moduli of rotundity and smoothness [PDF]
, 1999 summary:We study various notions of directional moduli of rotundity and when such moduli of rotundity of power type imply the underlying space is superreflexive.
Giles, John R. +2 more
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A new construction of Lupaş operators and its approximation properties
Advances in Difference Equations, 2021 The aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences u m $u_{m} $ and v m $v_{m}$ of functions.
Mohd Qasim +3 more
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Calabi–Yau threefolds and moduli of abelian surfaces I [PDF]
, 2001 We describe birational models and decide the rationality/unirationality of moduli spaces $\cal A$d (and $\cal A$levd) of (1, d)-polarized Abelian surfaces (with canonical level structure, respectively) for small values of d.
Sorin Popescu +3 more
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On Equivalence of Moduli of Smoothness
Journal of Approximation Theory, 1999 It is known that if \(f \in W^k_p\), then \[ \omega_m(f,t)_p \leq t \omega_{m-1}(f',t)_p \leq \cdots. \] The inverse statement with constants independent of \(f\) is not true in general. \textit{Y. Hu} and \textit{X. Yu} [SIAM J. Numer. Anal. 32, No. 5, 1428-1435 (1995; Zbl 0841.41007)] proved that the inverse holds true for splines \(S\) with equally ...
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Best approximation and moduli of smoothness: Computation and equivalence theorems [PDF]
, 2008 In this paper we investigate the trigonometric series with the β-general monotone coefficients. First, we study the uniform convergence criterion. The estimates of best approximations and moduli of smoothness of the series in uniform metrics are obtained
Tikhonov, Sergey
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