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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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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 ...
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Generalized Modulus of Smoothness and K-functional.
Communications on Applied Nonlinear AnalysisMany articles introduced about direct and inverse theorems interims of ordinary modulus of smoothness andK-functional. Here we shall define a generalized modulus of smoothness andK-functional, then we prove they are equivalent.
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Some properties of a new kind of modulus of smoothness
Zeitschrift für Analysis und ihre Anwendungen, 1984The modulus of smoothness \omega (f, \delta)_{\varphi, p} = \mathrm {sup}_{0 < h ≤ \delta} \| \Delta^2_{h, \varphi} \|_{L^p} has arisen during the investigation of positive operators of the Kantorovich type ...
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Nonperiodic modulus of smoothness corresponding to the Riesz derivative
Mathematical Notes, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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On Banaś modulus of smoothness and Gao Pythagorean constant of L(μ)
Journal of Mathematical Analysis and ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amini-Harandi, Alireza, Peyvaste, Malihe
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The Necessity of a New Kind of Modulus of Smoothness
1984A new type of modulus of smoothness is defined. It very much resembles the ordinary moduli of smoothness, only the increment in it varies togehter with the variable x. This new measurement provides a natural frame-work for the solution of several approximation-theoretical problems.
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On Jackson theorems for the generalized modulus of smoothness
1985The authors prove the following interesting theorem: Let \(\lambda >- 1,1\leq ...
Potapov, M. K., Fedorov, V. M.
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