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The Universal Approximation Capability of Double Flexible Approximate Identity Neural Networks

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Computer Engineering and Networking

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 277))

Abstract

This study investigates the universal approximation capability of three-layer feedforward double flexible approximate identity neural networks in the space of continuous functions with two variables. First, we propose double flexible approximate identity functions, which are a combination of double approximate identity functions and flexible approximate identity functions as investigated in our previous studies. Then, we prove that any continuous function f with two variables will converge to itself if it convolves with double flexible approximate identity. Finally, we prove a main theorem by using the obtained results.

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, USM, Pulau Pinang, Malaysia

    Saeed Panahian Fard & Zarita Zainuddin

Authors
  1. Saeed Panahian Fard
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  2. Zarita Zainuddin
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Corresponding author

Correspondence to Saeed Panahian Fard .

Editor information

Editors and Affiliations

  1. University of Texas at Dallas, Richardson, Texas, USA

    W. Eric Wong

  2. Chinese Academy of Sciences, Beijing, China, People’s Republic

    Tingshao Zhu

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© 2014 Springer International Publishing Switzerland

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Fard, S.P., Zainuddin, Z. (2014). The Universal Approximation Capability of Double Flexible Approximate Identity Neural Networks. In: Wong, W.E., Zhu, T. (eds) Computer Engineering and Networking. Lecture Notes in Electrical Engineering, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-319-01766-2_15

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  • DOI: https://doi.org/10.1007/978-3-319-01766-2_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01765-5

  • Online ISBN: 978-3-319-01766-2

  • eBook Packages: EngineeringEngineering (R0)

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