kantorovitch型抽样算子与近似

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-07-07 DOI:10.1002/mma.11192

Vijay Gupta, Vaibhav Sharma

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引用次数: 0

摘要

本文研究了广义kantorovich型抽样算子的收敛性。结合广义抽样算子和Kantorovich抽样算子，得到了新的复合算子，并估计了近似阶数。然后，我们根据一阶连续模和K $$ K $$ -泛函建立了收敛性的定量估计。我们还用广义抽样算子估计了这些算子的差值。此外，我们还研究了连续加权空间中的近似阶数。提供了满足必要假设的核的说明性示例。我们还通过图形示例和数值表证明了所提出的运算符的性能。最后，探讨了它们在数字图像处理中的潜在应用。

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Kantorovich-Type Sampling Operators and Approximation

In this article, we investigate the convergence behavior of generalized sampling operators of Kantorovich-type. By combining the generalized sampling operators and Kantorovich sampling operators, we obtain the new composition operators and estimate the order of approximation. Then, we establish quantitative estimates for convergence in terms of the first-order modulus of continuity and $K$ -functional. We also estimate the difference of these operators with generalized sampling operators. Moreover, we examine the order of approximation in the weighted space of continuity. Illustrative examples of kernels that meet the necessary assumptions are provided. We also demonstrate the performance of the proposed operators through graphical examples and numerical tables. Finally, we explore their potential applications in digital image processing.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.