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In this article, we study approximation properties of single hidden layer neural networks with weights varying in finitely many directions and with thresholds from an open interval. We obtain a necessary and simultaneously sufficient measure theoretic condition for density of such networks in the space of continuous functions. Further, we prove a density result for neural networks with a specifically constructed activation function and a fixed number of neurons. [ABSTRACT FROM PUBLISHER]

The goal of this article is to present multidimensional matrix characterization of geometrically dominated double sequences. We begin this characterization with the following definition of geometrically dominated factorable double sequence space. LetG″ denote a family of double complex number sequences that are dominated by a P-convergence geometric factorable double sequence, that is, This definition will be use to present the theorems similar to the following. The four-dimensional matrix is anG″ − l″ if and only ifand Other implication will also be presented. [ABSTRACT FROM AUTHOR]