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In this chapter we introduce for the first time the multivariate symmetrized and perturbed hyperbolic tangent 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.

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Approximation by Symmetrized and Perturbed Hyperbolic Tangent Activated Multivariate Convolution Operators

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  • 发表日期：

    2026年

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  • George A. Anastassiou

摘要

In this chapter we introduce for the first time the multivariate symmetrized and perturbed hyperbolic tangent 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.