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1.
In this paper we consider the trigonometric Fourier series with the β-general monotone coefficients. Necessary and sufficient conditions of L1-convergence for such a series, that is f−Sn=o(1), are obtained in terms of coefficients. 相似文献
2.
In the space of summable sequences we give an example of a one-dimensional affine subspace C such that the best Lp-approximations of 0 from C fail to converge as p↓1. We thus give an answer to this problem of convergence in infinite measure spaces. 相似文献
3.
Satit Saejung 《Journal of Mathematical Analysis and Applications》2006,320(2):543-548
In this paper, we prove that the moduli of W*-convexity, introduced by Ji Gao [J. Gao, The W*-convexity and normal structure in Banach spaces, Appl. Math. Lett. 17 (2004) 1381–1386], of a Banach space X and of the ultrapower of X itself coincide whenever X is super-reflexive. Moreover, we improve a sufficient condition for uniform normal structure of the space and its dual. This generalizes and strengthens the main results of [J. Gao, The W*-convexity and normal structure in Banach spaces, Appl. Math. Lett. 17 (2004) 1381–1386]. 相似文献
4.
Ferenc Móricz 《Journal of Mathematical Analysis and Applications》2008,342(2):1246-1249
We study the smoothness property of a function f with absolutely convergent Fourier series, and give best possible sufficient conditions in terms of its Fourier coefficients to ensure that f belongs to one of the Zygmund classes Λ∗(α) and λ∗(α) for some 0<α?2. This paper is a natural supplement to our earlier one [F. Móricz, Absolutely convergent Fourier series and function classes, J. Math. Anal. Appl. 324 (2) (2006) 1168-1177] under the same title, and we keep its notations. 相似文献
5.
This paper estimates upper and lower bounds for the approximation rates of iterated Boolean sums of multivariate Bernstein polynomials. Both direct and inverse inequalities for the approximation rate are established in terms of a certain K-functional. From these estimates, one can also determine the class of functions yielding optimal approximations to the iterated Boolean sums. 相似文献
6.
In this paper, we consider a Dirichlet problem involving the p(x)-Laplacian of the type We prove the existence of infinitely many non-negative solutions of the problem by applying a general variational principle due to B. Ricceri and the theory of the variable exponent Sobolev spaces. 相似文献
7.
Andrs Kro 《Journal of Approximation Theory》2009,159(1):85
Bernstein–Markov-type inequalities provide estimates for the norms of derivatives of algebraic and trigonometric polynomials. They play an important role in Approximation Theory since they are widely used for verifying inverse theorems of approximation. In the past decades these inequalities were extended to the multivariate setting, but the main emphasis so far was on the uniform norm. It is considerably harder to derive Bernstein–Markov-type inequalities in the Lq-norm, and it requires introduction of new methods. In this paper we verify certain Bernstein–Markov-type inequalities in Lq-norm on convex and star-like domains. Special attention is given to the question of how the geometry of the domain affects the corresponding estimates. 相似文献
8.
A great deal of research has been done on the aerodynamic characteristics of race cars competing in major racing series through out the world. Because of the competitive nature of motor sport, this research is usually not published until after it is obsolete. The teams operating at the minor league levels of the sport do not have the funding resources of the major series to perform aerodynamic research. In an effort to provide some information for teams competing in the minor league Formula Mazda racecar class, this study was conducted using the Star-CD CFD code to perform a turbulent simulation (using a k–ε model) of the airflow on the front and rear wings of a Formula Mazda car with different angles of attack and the effect of the ground on the front wing. Results are presented graphically, showing pressure and velocity distributions and lift (Cl) and drag coefficients (Cd) for the different cases. It was shown that the ground effect has a marked effect on the Cl and that the angle of attack has a significant effect on the lift and drag coefficients, and it was shown that an angle of 12 below the horizontal seems to indicate stalling conditions. It is suggested that this information, along with experimental validation, can be valuable for improving the optimum handling of these Formula Mazda race cars. 相似文献
9.
Ferenc Móricz 《Journal of Mathematical Analysis and Applications》2006,324(2):1168-1177
We study the smoothness property of a function f with absolutely convergent Fourier series, and give best possible sufficient conditions in terms of its Fourier coefficients to ensure that f belongs either to one of the Lipschitz classes Lip(α) and lip(α) for some 0<α?1, or to one of the Zygmund classes Λ∗(1) and λ∗(1). Our theorems generalize some of those by Boas [R.P. Boas Jr., Fourier series with positive coefficients, J. Math. Anal. Appl. 17 (1967) 463-483] and one by Németh [J. Németh, Fourier series with positive coefficients and generalized Lipschitz classes, Acta Sci. Math. (Szeged) 54 (1990) 291-304]. We also prove a localized version of a theorem by Paley [R.E.A.C. Paley, On Fourier series with positive coefficients, J. London Math. Soc. 7 (1932) 205-208] on the existence and continuity of the derivative of f. 相似文献
10.
In this paper, we study the existence of periodic solutions for a fourth-order p-Laplacian differential equation with a deviating argument as follows:
[φp(u″(t))]″+f(u″(t))+g(u(t−τ(t)))=e(t).