Results 211 to 220 of about 48,981 (245)

Lipschitz classes and convolution approximation processes

Mathematical Proceedings of the Cambridge Philosophical Society, 1981
For a continuous function f(x) on the reals or on the circle T (continuous and 2π periodic) we say that f(x) belongs to the generalized Lipschitz class, denoted by f ∈ Lip* α, ifwhere and Δhf(x) = f(x + ½h)−f(x−½h). For a convolution approximation process given bywherewe shall investigate equivalence relations between the asymptotic behaviour of (d/dx)
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Singular Integral Operator Involving Higher Order Lipschitz Classes

Mediterranean Journal of Mathematics, 2017
As in [\textit{R. Abreu-Blaya} et al., Bull. Braz. Math. Soc. (N.S.) 48, No. 2, 253--260 (2017; Zbl 1375.30061)] the poly-analytic Cauchy integral is extended to higher-order Lipschitz classes for simply connected plane domains with smooth boundary. Concentrating on the bi-analytic case the boundary integral with the Bitsadze kernel rather than the ...
Juan Bory-Reyes, Lianet De la Cruz-Toranzo, Ricardo Abreu-Blaya   +2 more
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Boundary interpolation in weak Lipschitz classes

Journal of Mathematical Sciences, 2009
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Lipschitz classes on finite dimensional groups

Mathematical Proceedings of the Cambridge Philosophical Society, 1969
In this paper G will denote a compact metric Abelian group having finite topological dimension, dim G. The discrete dual group of G will be denoted by Γ. The metric on G will be denoted by d(x, y), or |x-y| since translation-invariance is assumed.
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Bernstein-type operators, convexity and Lipschitz classes

Approximation Theory and its Applications, 1995
The authors study the monotonicity properties of the sequences of some Bernstein-type operators, relative to convex functions, as well as the preservation properties of Lipschitz classes for these operators. They start from a class of Bernstein-Schnabl type operators and give several illustrations for the operators of Bernstein, Stancu and Cheney ...
DELLA VECCHIA, Biancamaria, I. Rasa
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Rational approximation to Lipschitz and Zygmund classes

Constructive Approximation, 1992
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Borwein, P. B., Zhou, S. P.
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Lipschitz classes on 0-dimensional groups

Mathematical Proceedings of the Cambridge Philosophical Society, 1967
1. Let G be a compact metric 0-dimensional Abelian group. Its dual or character group Γ is a discrete countable torsion group. We denote elements of G by x, of Γ by y, the value of the character y at x by (x, y), and the Fourier transform of f by
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Specific properties of Lipschitz class functions

Acta Mathematica Hungarica
The authors find two conditions on an orthonormal system (ONS) in \( L_2(0,1) \) which imply that for arbitrary \( f \in\) Lip 1 and for any \( \varepsilon\in (0,1) \) the series \[\sum_{k=1}^{\infty} C_k^2(f)k^{2(1-\varepsilon)}\] converges (here \( C_k(f) \) are the Fourier coefficients with respect to that ONS).
Kashibadze, A., Tsagareishvili, V.
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Local and global Lipschitz classes

1987
Let h be a modulus of continuity, i.e. u is a concave positive and increasing function. If D is a domain in \({\mathbb{R}}^ n\), then a function \(u: D\to {\mathbb{R}}\) is said to belong to the local Lipschitz class loc Lip\({}_ h(D)\) if there is \(b\in (0,1)\) and M such that \(| u(x)- u(y)| \leq M h(| x-y|)\) for all \(x\in D\) and \(y\in D\) with \
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Strong Approximation and Generalized Lipschitz Classes

1981
Recently several papers (see e.g. [2], [3, [5], [7, [10]) deal with problems of imbedding of classes of functions connected with strong approximation of Fourier series. At such problems the main question is to find conditions implying that a certain class of functions should be imbedded into another one, and one of the classes in question is determined
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