Approximation by Symmetrized and Perturbed Hyperbolic Tangent Activated Convolution-Type Operators

George A. Anastassiou ()
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George A. Anastassiou: Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA

Mathematics, 2024, vol. 12, issue 20, 1-48

Abstract: In this article, for the first time, the univariate symmetrized and perturbed hyperbolic tangent activated convolution-type operators of three kinds are introduced. Their approximation properties are presented, i.e., the quantitative convergence to the unit operator via the modulus of continuity. It follows the global smoothness preservation of these operators. The related iterated approximation as well as the simultaneous approximation and their combinations, are also extensively presented. Including differentiability and fractional differentiability into our research produced higher rates of approximation. Simultaneous global smoothness preservation is also examined.

Keywords: symmetrized and perturbed hyperbolic tangent; convolution-type operator; Caputo fractional derivative; quantitative approximation; global smoothness preservation; simultaneous approximation; iterated approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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