共查询到20条相似文献,搜索用时 0 毫秒
1.
Approximation of Generalized Szász-Mirakjan OperatorChengHailal(程海来)(AnhuiInstituteofTechnology)Abstract:Inthispaper,theautho... 相似文献
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The main goal of this paper is to introduce Durrmeyer modifications for the generalized Szász–Mirakyan operators defined in (Aral et al., in Results Math 65:441–452, 2014). The construction of the new operators is based on a function \(\rho \) which is continuously differentiable \(\infty \) times on \( \left[ 0,\infty \right) ,\) such that \(\rho \left( 0\right) =0\) and \( \inf _{x\in \left[ 0,\infty \right) }\rho ^{\prime }\left( x\right) \ge 1.\) Involving the weighted modulus of continuity constructed using the function \( \rho \), approximation properties of the operators are explored: uniform convergence over unbounded intervals is established and a quantitative Voronovskaya theorem is given. Moreover, we obtain direct approximation properties of the operators in terms of the moduli of smoothness. Our results show that the new operators are sensitive to the rate of convergence to f, depending on the selection of \(\rho .\) For the particular case \(\rho \left( x\right) =x\), the previous results for classical Szász-Durrmeyer operators are captured. 相似文献
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《Indagationes Mathematicae》2017,28(4):854-862
Every Archimedean Riesz space can be embedded as an order dense subspace of some , the Riesz space of all extended continuous functions on a Stonean space , called its Maeda–Ogasawara space. Furthermore, it is a fact that every Riesz homomorphism between spaces of ordinary continuous functions on compact Hausdorff spaces is a weighted composition operator. We prove that a generalised statement holds for Maeda–Ogasawara spaces and refine these results in case the homomorphism preserves order limits. 相似文献
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Vagif Sabir Guliyev Turhan Karaman Rza Chingiz Mustafayev Ayhan Şerbetçi 《Czechoslovak Mathematical Journal》2014,64(2):365-386
In this paper, the boundedness of a large class of sublinear commutator operators T b generated by a Calderón-Zygmund type operator on a generalized weighted Morrey spaces \({M_{p,\varphi }}(w)\) with the weight function w belonging to Muckenhoupt’s class A p is studied. When 1 < p < ∞ and b ∈ BMO, sufficient conditions on the pair (φ 1, φ 2) which ensure the boundedness of the operator T b from \({M_{p,\varphi 1}}(w)\) to \({M_{p,\varphi 2}}(w)\) are found. In all cases the conditions for the boundedness of T b are given in terms of Zygmund-type integral inequalities on (φ 1, φ 2), which do not require any assumption on monotonicity of φ 1(x, r), φ 2(x, r) in r. Then these results are applied to several particular operators such as the pseudo-differential operators, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator. 相似文献
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The so-called Bernstein operators were introduced by S.N. Bernstein in 1912 to give a constructive proof of Weierstrass? theorem. We show how to extend his result to Müntz spaces on positive intervals. 相似文献
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V. P. Orlov 《Mathematical Notes》1977,21(6):428-433
A differential operator ?, arising from the differential expression $$lv(t) \equiv ( - 1)^r v^{[n]} (t) + \sum\nolimits_{k = 0}^{n - 1} {p_k } (t)v^{[k]} (t) + Av(t),0 \leqslant t \leqslant 1,$$ , and system of boundary value conditions $$P_v [v] = \sum\nolimits_{k = 0}^{n_v } {\alpha _{vk} } r^{[k]} (1) = 0.v - 1, \ldots ,\mu ,0 \leqslant \mu< n$$ is considered in a Banach space E. Herev [k](t)=(a(t) d/dt) k v(t)a(t) being continuous fort?0, α(t) >0 for t > 0 and \(\int_0^1 {\frac{{dz}}{{a(z)}} = + \infty ;}\) the operator A is strongly positive in E. The estimates , are obtained for ?: n even, λ varying over a half plane. 相似文献
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Peter R. Mercer 《Integral Equations and Operator Theory》1998,31(4):482-488
It is shown that a compact composition operator on a weighted Bergman space over a smoothly bounded strongly convex domain in
n
can have no angular derivative. Also, sufficient conditions for the boundedness and the compactness of composition operators defined on Hardy and weighted Bergman spaces are obtained, for situations in which each of the target spaces is enlarged in a natural way. 相似文献
10.
Xinxing Wu 《Czechoslovak Mathematical Journal》2014,64(1):105-114
During the last ten some years, many research works were devoted to the chaotic behavior of the weighted shift operator on the Köthe sequence space. In this note, a sufficient condition ensuring that the weighted shift operator B w n : λ p (A) → λ p (A) defined on the Köthe sequence space λ p (A) exhibits distributional ?-chaos for any 0 < ? < diamλ p (A) and any n ∈ ? is obtained. Under this assumption, the principal measure of B w n is equal to 1. In particular, every Devaney chaotic shift operator exhibits distributional ?-chaos for any 0 < ? < diam λ p (A). 相似文献
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We investigate spectral properties of integral operators of the form
acting on Banach spaces of analytic functions on the unit disc. In the case that g is a rational function, analytic on the unit disc, we obtain the spectrum, essential spectrum and index of Sg. Finally, we give examples of such operators pertaining to hyponormality.
Received: 30 August 2004; revised: 25 January 2005 相似文献
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Interpolation theorems on weighted Lorentz martingale spaces 总被引:2,自引:0,他引:2
Yong JIAO~ Li-ping FAN Pei-de LIU School of Mathematics Statistics Wuhan University Wuhan China 《中国科学A辑(英文版)》2007,50(9):1217-1226
In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation theorems,we obtain some inequalities on martingale transform operator. 相似文献
13.
Haibo Lin 《Archiv der Mathematik》2016,106(3):275-284
Let \({\varphi}\) be a Musielak–Orlicz function satisfying that, for any \({(x,\,t)\in{\mathbb R}^n \times [0, \infty)}\), \({\varphi(\cdot,\,t)}\) belongs to the Muckenhoupt weight class \({A_\infty({\mathbb R}^n)}\) with the critical weight exponent \({q(\varphi) \in [1,\,\infty)}\) and \({\varphi(x,\,\cdot)}\) is an Orlicz function with uniformly lower type \({p^{-}_{\varphi}}\) and uniformly upper type \({p^+_\varphi}\) satisfying \({q(\varphi) < p^{-}_{\varphi}\le p^{+}_{\varphi} < \infty}\). In this paper, the author obtains a sharp weighted bound involving \({A_\infty}\) constant for the Hardy–Littlewood maximal operator on the Musielak–Orlicz space \({L^{\varphi}}\). This result recovers the known sharp weighted estimate established by Hytönen et al. in [J. Funct. Anal. 263:3883–3899, 2012]. 相似文献
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N.I. Mahmudov 《Applied Mathematics Letters》2011,24(7):1231-1238
In this paper, the order of simultaneous approximation and Voronovskaja-type theorems with quantitative estimate for complex Bernstein–Durrmeyer-type polynomials attached to analytic functions on compact disks are obtained. Our results show that extension of the complex Bernstein–Durrmeyer-type polynomials from real intervals to compact disks in the complex plane extends approximation properties. 相似文献
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XINFENG WU 《Proceedings Mathematical Sciences》2014,124(1):81-92
In this paper, we introduce weighted Besov spaces and weighted Triebel–Lizorkin spaces associated with different homogeneities and prove that the composition of two Calderón–Zygmund operators is bounded on these spaces. This extends a recent result in Han et al, Revista Mat. Iber. 相似文献
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Dansheng Yu 《Acta Mathematica Hungarica》2013,141(1-2):132-149
We introduce a new type of Kantorovich–Bernstein operators. Direct and converse theorems and a Voronovskaya-type relation are given for the weighted approximation with Jacobi weights w(x)=x α (1?x) β by the new operator. None of the results involved have the restriction ${\alpha,\beta<1-\frac{1}{p}}$ . 相似文献
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Н. т. АМАНОВ 《Analysis Mathematica》1992,18(3):167-184