Abstract Univariate Neural Network Approximation Using a q-Deformed and λ-Parametrized Hyperbolic Tangent Activation Function

In this work, we perform univariate approximation with rates, basic and fractional, of continuous functions that take values into an arbitrary Banach space domain on a closed interval or all reals, by quasi-interpolation neural network operators. These approximations are achieved deriving Jackson-type inequalities via the first modulus continuity hand function its abstract integer derivative Caputo fractional derivatives. Our operators expressed density based q-deformed λ-parameterized hyperbolic tangent activation sigmoid function. The convergences pointwise uniform. associated feed-forward networks one hidden layer.