{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T13:59:17Z","timestamp":1725890357577},"publisher-location":"Berlin, Heidelberg","reference-count":15,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642344749"},{"type":"electronic","value":"9783642344756"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-34475-6_49","type":"book-chapter","created":{"date-parts":[[2012,11,5]],"date-time":"2012-11-05T03:33:26Z","timestamp":1352086406000},"page":"409-415","source":"Crossref","is-referenced-by-count":13,"title":["Double Approximate Identity Neural Networks Universal Approximation in Real Lebesgue Spaces"],"prefix":"10.1007","author":[{"given":"Zarita","family":"Zainuddin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saeed Panahian","family":"Fard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"49_CR1","first-page":"124","volume":"29","author":"N. Dong","year":"2009","unstructured":"Dong, N., Ling, L.J.: L\n                  \n                    p\n                  (K) Approximation problems in system identification with RBF neural networks. Mathematical Research and Exposition\u00a029, 124\u2013128 (2009)","journal-title":"Mathematical Research and Exposition"},{"key":"49_CR2","volume-title":"Operation calculus in two variable and its applications","author":"V.A. Ditkin","year":"1962","unstructured":"Ditkin, V.A., Prudnikov, A.P.: Operation calculus in two variable and its applications. Pergamon Press, New York (1962)"},{"key":"49_CR3","doi-asserted-by":"publisher","first-page":"1897","DOI":"10.1016\/j.camwa.2003.06.008","volume":"47","author":"N. Hahm","year":"2004","unstructured":"Hahm, N., Hong, B.I.: An approximation by neural networks with a fixed weight. Computers and Mathematics with Applications\u00a047, 1897\u20131903 (2004)","journal-title":"Computers and Mathematics with Applications"},{"key":"49_CR4","unstructured":"Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalites. Cambridge University Press (1988)"},{"key":"49_CR5","doi-asserted-by":"crossref","unstructured":"Hect-Nielsen, R.: Theory of the back propagation neural networks. In: Proceedings International Joint Conference on Neural Networks, vol.\u00a01, pp. 593\u2013611 (1989)","DOI":"10.1109\/IJCNN.1989.118638"},{"key":"49_CR6","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1016\/0893-6080(91)90009-T","volume":"4","author":"K. Hornik","year":"1991","unstructured":"Hornik, K.: Approximation capabilities of multilayer feedforward networks. Neural Networks\u00a04, 251\u2013257 (1991)","journal-title":"Neural Networks"},{"key":"49_CR7","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","volume":"2","author":"K. Hornik","year":"1989","unstructured":"Hornik, K., Stinchombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks\u00a02, 359\u2013366 (1989)","journal-title":"Neural Networks"},{"key":"49_CR8","unstructured":"Jones, F.: Lebesgue integration on Euclidean space. Jones and Bartlett (1993)"},{"key":"49_CR9","doi-asserted-by":"crossref","unstructured":"Lebedev, V.: An introduction to functional analysis and computational mathematics. Birkh\u00e4user (1997)","DOI":"10.1007\/978-1-4612-4128-7"},{"key":"49_CR10","unstructured":"Li, F.: Function approximation by neural networks. In: Proceedings 5th International Symposium on Neural Networks, pp. 348\u2013390 (2008)"},{"key":"49_CR11","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1016\/S0893-6080(02)00227-7","volume":"16","author":"Y. Liao","year":"2003","unstructured":"Liao, Y., Fang, S.C., Nuttle, H.L.W.: Relaxed conditions for radial-basis function networks to be universal approximators. Neural Networks\u00a016, 1019\u20131028 (2003)","journal-title":"Neural Networks"},{"key":"49_CR12","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1016\/S0893-6080(98)00068-9","volume":"11","author":"S. Suzuki","year":"1998","unstructured":"Suzuki, S.: Constructive function approximation by three-layer artificial neural networks. Neural Networks\u00a011, 1049\u20131058 (1998)","journal-title":"Neural Networks"},{"key":"49_CR13","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.1109\/72.728353","volume":"9","author":"C. Turchetti","year":"1998","unstructured":"Turchetti, C., Conti, M., Crippa, P., Orcioni, S.: On the approximation of stochastic processes by approximate identity neural networks. IEEE Transactions on Neural Networks\u00a09, 1069\u20131085 (1998)","journal-title":"IEEE Transactions on Neural Networks"},{"key":"49_CR14","doi-asserted-by":"crossref","DOI":"10.1201\/b15702","volume-title":"Measure and Integral","author":"R.L. Wheeden","year":"1977","unstructured":"Wheeden, R.L., Zygmund, A.: Measure and Integral. Marcel Dekker, New York (1977)"},{"key":"49_CR15","doi-asserted-by":"crossref","unstructured":"Wu, W., Nan, D., Li, Z., Long, J., Wang, J.: Approximation to compact set of functions by feedforward neural networks. In: 20th International Joint Conference on Neural Networks, pp. 1222\u20131225 (2007)","DOI":"10.1109\/IJCNN.2007.4371132"}],"container-title":["Lecture Notes in Computer Science","Neural Information Processing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-34475-6_49.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,4]],"date-time":"2021-05-04T08:53:50Z","timestamp":1620118430000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-34475-6_49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642344749","9783642344756"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-34475-6_49","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2012]]}}}