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A generalized modulus of smoothness
Proceedings of the American Mathematical Society, 2014We construct moduli of smoothness that generalize the well-known classical moduli and possess similar properties. They are related to a linear differential operator L L
Draganov, Borislav R., Ivanov, Kamen G.
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On a third-order modulus of smoothness
Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science, 2023In this paper we define a new third-order modulus of smoothness and we prove the conservation by Stancu operators of the Lipschitz classes defined with this modulus.
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Modulus of Smoothness and Approximation Theorems in Clifford Analysis
Complex Analysis and Operator Theory, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Modulus of Smoothness and Approximation in Morrey–Banach Spaces
Mediterranean Journal of MathematicsThe author extends the approximation inequalities of the modulus of smoothness to Morrey-Banach spaces by estimating the modulus of smoothness by the derivatives and the approximation by the trigonometric polynomials. As special, cases he obtains the corresponding results for classical Morrey spaces, for Lorentz-Morrey spaces, for Orlicz-Morrey spaces ...
Kwok-Pun Ho
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A modulus of smoothness on the unit sphere
Journal d'Analyse Mathématique, 1999For functions on \(S^{d-1}\) (the unit sphere in \(\mathbb{R}^d\)), and, in particular, for \(f \in L_p(S^{d-1 ...
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The Modulus of Smoothness in Metric Spaces and Related Problems
Potential Analysis, 2010The paper studies generalized Besov and Sobolev spaces of functions on a metric measure space. The definition involves a rather general modulus of smoothness with two Banach lattices \(E\) and \(F\), and an auxiliary nondecreasing function. Let \(f^*\) stand for the decreasing rearrangement of \(f\) on \((0,\mu(X))\), and \(f^{**}\) for its maximal ...
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The Modulus of Smoothness and Discrete Data in a Square Domain
IMA Journal of Numerical Analysis, 1988This paper relates to a function f on a two-dimensional square domain that is finite, infinite, or semi-infinite. It is shown that, if the second difference of f with respect to a uniform square lattice of mesh- size \(2^{-n}\) is uniformly of order \(2^{-n\alpha}\), with ...
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Complex modulus and compliance for airway smooth muscle cells
Physical Review E, 2020A cell can be described as a complex viscoelastic material with structural relaxations that is modulated by thermal and chemically nonequilibrium processes. Tissue morphology and function rely upon cells' physical responses to mechanical force. We measured the frequency-dependent mechanical relaxation response of adherent human airway smooth muscle ...
Peter Berntsen +3 more
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On the K-Functional for the Mixed Generalized Modulus of Smoothness
Mathematical Notes, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Local smoothness of an analytic function compared to the smoothness of its modulus
St. Petersburg Mathematical Journal, 2014Summary: Let \(\Phi\) be a function analytic in the disk and continuous up to the boundary, and let its modulus of continuity satisfy the Hölder condition of order \(\alpha ...
Vasin, A. V. +2 more
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