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In this chapter are introduced for the first time the univariate symmetrized and perturbed hyperboolic tangent activated convolution type operators of three kinds. Their approximation properties are presented, that is the quantitative convergence to the unit operator via the modulus of continuity. It follows the global smoothness preservation of these operators.

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Degree of Approximation by Symmetrized and Perturbed Hyperbolic Tangent Activated Convolution Operators

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  • 发表日期：

    2026年

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  • George A. Anastassiou

摘要

In this chapter are introduced for the first time the univariate symmetrized and perturbed hyperboolic tangent activated convolution type operators of three kinds. Their approximation properties are presented, that is the quantitative convergence to the unit operator via the modulus of continuity. It follows the global smoothness preservation of these operators.