Convergence in distribution of the Bernstein–Durrmeyer kernel and pointwise convergence of a generalised operator for functions of bounded variation

IF 0.9 3区 数学 Q2 MATHEMATICS
Mohammed Taariq Mowzer
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引用次数: 0

Abstract

We study the convergence of Bernstein type operators leading to two results. The first: The kernel Kn of the Bernstein–Durrmeyer operator at each point x(0,1) — that is Kn(x,t)dt — once standardised converges to the normal distribution. The second result computes the pointwise limit of a generalised Bernstein–Durrmeyer operator applied to — possibly discontinuous — functions f of bounded variation.

伯恩斯坦-达尔迈耶核分布的收敛性和有界变化函数广义算子的点收敛性
我们对伯恩斯坦型算子的收敛性进行了研究,得出了两个结果。第一个结果:伯恩斯坦-杜尔迈耶算子在每一点 x∈(0,1) 的核 Kn(即 Kn(x,t)dt)一旦标准化,就会收敛于正态分布。第二个结果是计算应用于有界变化函数 f(可能不连续)的广义伯恩斯坦-德尔迈尔算子的点极限。
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来源期刊
CiteScore
1.90
自引率
11.10%
发文量
55
审稿时长
6-12 weeks
期刊介绍: The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.
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