矢量值谢泼德过程：求和近似

IF 1.9 3区数学 Q1 MATHEMATICS, APPLIED

Axioms Pub Date : 2023-12-15 DOI:10.3390/axioms12121124

O. Duman, B. Vecchia

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引用次数: 0

摘要

在这项工作中，矢量值连续函数在单位超立方体上被谢泼德算子均匀逼近。如果 λ 表示 Shepard 算子的常规参数，m 是超立方体的维数，那么我们的结果表明，当 λ≥m+1 时，可以通过这些算子得到连续向量值函数的均匀近似值。通过使用三维参数图，我们说明了对某些矢量值函数的这种均匀逼近。最后，我们研究了正则求和过程对近似的影响，并说明了它们的动机。

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Vector-Valued Shepard Processes: Approximation with Summability

In this work, vector-valued continuous functions are approximated uniformly on the unit hypercube by Shepard operators. If λ denotes the usual parameter of the Shepard operators and m is the dimension of the hypercube, then our results show that it is possible to obtain a uniform approximation of a continuous vector-valued function by these operators when λ≥m+1. By using three-dimensional parametric plots, we illustrate this uniform approximation for some vector-valued functions. Finally, the influence in approximation by regular summability processes is studied, and their motivation is shown.

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来源期刊

Axioms Mathematics-Algebra and Number Theory

自引率

10.00%

发文量

604

审稿时长

11 weeks

期刊介绍： Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.