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Analyses for L p[a, b]-norm approximation capability of flexible approximate identity neural networks

  • ICONIP 2012
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Abstract

This study investigates the universal approximation capability of a three-layered feedforward flexible approximate identity neural networks under the L p[a, b]-norm. We are motivated to study such a problem by the fact that the L p[a, b]-norm has the capability of improving approximation performance significantly. Using flexible approximate identity functions as introduced in our previous study, we prove that any Lebesgue integrable function on the closed and bounded real interval [a, b] will converge to itself under the L p[a, b]-norm if it convolves with flexible approximate identity functions. Using this result, we also establish a main theorem. The proof of the main theorem is in the framework of the theory of \(\epsilon\)-net.

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Acknowledgments

The authors wish to thank the anonymous referees for their precious comments and suggestions. This work was supported by Universiti Sains Malaysia (1001/PMATHS/811161).

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia

    Saeed Panahian Fard & Zarita Zainuddin

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  1. Saeed Panahian Fard
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  2. Zarita Zainuddin
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Correspondence to Zarita Zainuddin.

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Panahian Fard, S., Zainuddin, Z. Analyses for L p[a, b]-norm approximation capability of flexible approximate identity neural networks. Neural Comput & Applic 24, 45–50 (2014). https://doi.org/10.1007/s00521-013-1493-9

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  • DOI: https://doi.org/10.1007/s00521-013-1493-9

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