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Multivariate Approximation by Parametrized Logistic Activated Multidimensional Convolution Type Operators

Department of Mathematical Sciences, University of Memphis, Memphis, TN

* Corresponding Author
Annals of Communications in Mathematics 2024
, 7 (2),
128-159.
https://doi.org/10.62072/acm.2024.070206
Received: 13 May 2024 |
Accepted: 20 Jun 2024 |
Published: 30 Jun 2024

Abstract

In this work we introduce for the first time the multivariate parametrized logistic activated convolution type operators in three kinds. We present their approximation properties, that is the quantitative convergence to the unit operator via the multivariate modulus of continuity. We continue with the multivariate global smoothness preservation of these operators. We present extensively the related multivariate iterated approximation, as well as, the multivariate simultaneous approximation and their combinations. Using differentiability into our research, we are producing higher speeds of approximation, multivariate simultaneous global smoothness preservation is also studied.

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Cite This Article

Multivariate Approximation by Parametrized Logistic Activated Multidimensional Convolution Type Operators.

Annals of Communications in Mathematics,

2024,
7 (2):
128-159.
https://doi.org/10.62072/acm.2024.070206
  • Creative Commons License
  • Copyright (c) 2023 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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