Approximation results by multivariate Kantorovich-type neural network sampling operators in Lebesgue spaces with variable exponents

In this paper, we study convergence of a family of Neural Network operators of the type Kantorovich with sigmoidal activation functions. Such operators are multivariate. We study the problem of convergence in the setting of Lebesgue space with variable exponent \(L^{p(\cdot )}(\mathcal {R})\) $L^{p(·)}(\mathcal{R})$ with \(1\le p^-\le p(x)\le p^+<+\infty , \forall x\in \mathcal {R}\) $1\le p^{-}\le p(x)\le p^{+}<+\infty ,\forall x\in \mathcal{R}$ . Also, the pointwise and uniform convergence for functions belonging to suitable spaces are proved. In particular, our results apply to \(L^p\) $L^p$ -spaces. Multivariate Neural Network approximation finds applications, typically in neurocomputing processes.