q-Analogue of a Kantorovitch Variant of an Operator Defined by Stancu

IF 0.3 Q4 MATHEMATICS
P. N. Agrawal, Arun Kajla, Abhishek Kumar
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引用次数: 2

Abstract

The purpose of this paper is to introduce a new kind of q −Stancu-Kantorovich type operators and study its various approximation properties. We establish some local direct theorems, e.g., Voronovskaja type asymptotic theorem, global approximation and an estimate of error by means of the Lipschitz type maximal function and the Peetre K-functional. We also consider a n th-order generalization of these operators and study its approximation properties. Next, we define a bivariate case of these operators and investigate the order of convergence by means of moduli of continuity and the elements of Lipschitz class. Furthermore, we consider the associated Generalized Boolean Sum (GBS) operators and examine the approximation degree for functions in a Bögel space. Some numerical examples to illustrate the convergence of these operators to certain functions are also given.

由Stancu定义的算子的Kantorovitch变体的q-模拟
本文的目的是引入一类新的q−Stancu-Kantorovich型算子,并研究其各种逼近性质。我们建立了一些局部直接定理,如Voronovskaja型渐近定理、全局逼近以及利用Lipschitz型极大函数和Peetre K-泛函的误差估计。我们还考虑了这些算子的n阶推广,并研究了它的逼近性质。接下来,我们定义了这些算子的二元情况,并通过连续模和Lipschitz类的元素研究了收敛阶。此外,我们考虑了相关的广义布尔和(GBS)算子,并检验了Bögel空间中函数的逼近度。文中还给出了一些数值例子来说明这些算子对某些函数的收敛性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
23
期刊介绍: Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.
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