Results 11 to 20 of about 33 (27)
Journal of Function Spaces, Volume 2015, Issue 1, 2015., 2015 Authors define w∗ nearly dentable Banach space. Authors study Radon‐Nikodym property, approximative compactness and continuity metric projector operator in w∗ nearly dentable space. Moreover, authors obtain some examples of w∗ nearly dentable space in Orlicz function spaces.
Shaoqiang Shang, Yunan Cui, Ismat Beg
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Uniform Approximation of Periodical Functions by Trigonometric Sums of Special Type
International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014 The approximation characteristics of trigonometric sums Un,pψ of special type on the class Cβ,∞ψ of (ψ, β)‐differentiable (in the sense of A. I. Stepanets) periodical functions are studied. Because of agreement between parameters of approximative sums and approximated classes, the solution of Kolmogorov‐Nikol’skii problem is obtained in a sufficiently ...
A. S. Serdyuk +3 more
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Weighted Hardy‐Type Inequalities in Variable Exponent Morrey‐Type Spaces
Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013 We study the p(·) → q(·) boundedness of weighted multidimensional Hardy‐type operators Hwα· and ℋwα· of variable order α(x), with radial weight w(|x|), from a variable exponent locally generalized Morrey space ℒp(·),φ(·)(ℝn, w) to another ℒq(·),ψ(·)(ℝn, w). The exponents are assumed to satisfy the decay condition at the origin and infinity.
Dag Lukkassen +4 more
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On the approximation by trigonometric polynomials in weighted Lorentz spaces
Journal of Function Spaces, Volume 8, Issue 1, Page 67-86, 2010., 2010 We obtain estimates of structural characteristics of 2π‐periodic functions by the best trigonometric approximations in weighted Lorentz spaces, and show that the order of generalized modulus of smoothness depends not only on the rate of the best approximation, but also on the metric of the spaces.
Vakhtang Kokilashvili +2 more
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Journal of Function Spaces, Volume 8, Issue 3, Page 215-244, 2010., 2010 We consider non‐standard Hölder spaces Hλ(⋅)(X) of functions f on a metric measure space (X, d, μ), whose Hölder exponent λ(x) is variable, depending on x ∈ X. We establish theorems on mapping properties of potential operators of variable order α(x), from such a variable exponent Hölder space with the exponent λ(x) to another one with a “better ...
Natasha Samko +3 more
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New Characterization for Nonlinear Weighted Best Simultaneous Approximation
International Journal of Mathematics and Mathematical Sciences, Volume 2009, Issue 1, 2009., 2009 This paper is concerned with the problem of a wide class of weighted best simultaneous approximation in normed linear spaces, and it establishes a new characterization result for the class of approximation by virtue of the notion of simultaneous regular point.
Xianfa Luo +3 more
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Journal of Function Spaces, Volume 7, Issue 1, Page 61-89, 2009., 2009 In connection with application to various problems of operator theory, we study almost monotonic functions w(x, r) depending on a parameter x which runs a metric measure space X, and the so called index numbers m(w, x), M(w, x) of such functions, and consider some generalized Zygmund, Bary, Lozinskii and Stechkin conditions.
Natasha Samko, Vladimir D. Stepanov
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The maximal operator in weighted variable spaces Lp(⋅)
Journal of Function Spaces, Volume 5, Issue 3, Page 299-317, 2007., 2007 We study the boundedness of the maximal operator in the weighted spaces Lp(⋅)(ρ) over a bounded open set Ω in the Euclidean space ℝn or a Carleson curve Γ in a complex plane. The weight function may belong to a certain version of a general Muckenhoupt‐type condition, which is narrower than the expected Muckenhoupt condition for variable exponent, but ...
Vakhtang Kokilashvili +3 more
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Modulus of smoothness and theorems concerning approximation on compact groups
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 20, Page 1251-1260, 2003., 2003 We consider the generalized shift operator defined by (Shuf)(g) = ∫Gf(tut−1g)dt on a compact group G, and by using this operator, we define spherical modulus of smoothness. So, we prove Stechkin and Jackson‐type theorems.
H. Vaezi, S. F. Rzaev
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Concepts of generalized bounded variation and the theory of Fourier series
International Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 2, Page 223-244, 1986., 1986 The aim of this article is to unify a large part of present knowledge about the behaviour of Fourier series of functions of generalized bounded variation. The connections between various concepts are discussed, particular attention being payed to those due to Waterman and Chanturiya.
M. Avdispahić
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