Interpolation for neural-network operators activated with a generalized logistic-type function
Hande Uyan, Abdullah Ozan Aslan, Seda Karateke, İbrahim Büyükyazıcı · Journal of Inequalities and Applications · 2024
Abstract This paper defines a family of neural-network interpolation operators. The first derivative of generalized logistic-type functions is considered as a density function. Using the first-order uniform approximation theorem for continuous functions defined on the finite intervals, the interpolation properties of these operators are presented. A Kantorovich-type variant of the operators $F_{n}^{a,\varepsilon} $ F n a , ε is also introduced. The approximation of Kantorovich-type operators in $L_{P}$ L P spaces with $1 \leq p\leq \infty $ 1 ≤ p ≤ ∞ is studied. Further, different combinations of the parameters of our generalized logistic-type activation function $\theta _{s, a}$ θ s , a are examined to see which parameter values might give us a more efficient activation function. By choosing suitable parameters for the operator $F_{n}^{a,\varepsilon} $ F n a , ε and the Kantorovich variant of the operator $F_{n}^{a,\varepsilon} $ F n a , ε , the approximation of various function examples is studied.