caa a22 4500 605469776 CHVBK 20210128100324.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00500-014-1449-8 doi (NATIONALLICENCE)springer-10.1007/s00500-014-1449-8 The universal approximation capabilities of double 2 $$\pi $$ π -periodic approximate identity neural networks [Elektronische Daten] [Saeed Panahian Fard, Zarita Zainuddin] The purpose of this study is to investigate the universal approximation capabilities of a certain class of single-hidden-layer feedforward neural networks, which is called double 2 $$\pi $$ π -periodic approximate identity neural networks. Using double 2 $$\pi $$ π -periodic approximate identity, several theorems concerning the universal approximation capabilities of the networks are proved. The proofs of these theorems are sketched based on the double convolution linear operators and the definition of $$\epsilon $$ ϵ -net. The obtained results are divided into two categories. First, the universal approximation capability of the networks is shown in the space of continuous bivariate 2 $$\pi $$ π -periodic functions. Then, universal approximation capability of the networks is extended to the space of pth-order Lebesgue-integrable bivariate 2 $$\pi $$ π -periodic functions. These results can be interpreted as an extension of the universal approximation capabilities established for single-hidden-layer feedforward neural networks. Springer-Verlag Berlin Heidelberg, 2014 Double 2 $$\pi $$ π -periodic approximate identity nationallicence Double 2 $$\pi $$ π -periodic approximate identity neural networks nationallicence Universal approximation nationallicence Uniform convergence nationallicence Generalized Minkowski inequality nationallicence Panahian Fard Saeed School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia aut Zainuddin Zarita School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia aut Soft Computing Springer Berlin Heidelberg 19/10(2015-10-01), 2883-2890 1432-7643 19:10<2883 2015 19 500 https://doi.org/10.1007/s00500-014-1449-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00500-014-1449-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Panahian Fard Saeed School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia aut NATIONALLICENCE 700 1- Zainuddin Zarita School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia aut NATIONALLICENCE 773 0- Soft Computing Springer Berlin Heidelberg 19/10(2015-10-01), 2883-2890 1432-7643 19:10<2883 2015 19 500