Approximation by symmetrized and perturbed hyperbolic tangent activated convolutions as positive linear operators

Key Points

• The study establishes new approximation properties for hyperbolic tangent activated convolutions, highlighting their effectiveness in various mathematical contexts.
• Quantitative convergence to the unit operator is achieved using the modulus of continuity, showcasing a significant breakthrough in approximation theory.
• Simultaneous and iterated approximation methods are analyzed, expanding the theoretical framework of these operators.
• The approach utilizes positive linear operators to derive results that may impact future research in mathematical approximation techniques.