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Approximation of integrable functions based on \(\phi -\)transform

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Abstract

Let \(E\) be a bounded subset of real line which contains its infimum and supremum. In this paper, we have defined the \(\phi -\)transform and its inverse, where \(\phi \) is a function from \(E\) into \((0,1]\). We will have shown that real-valued integrable functions on \([a, b]\) and real-valued continuous functions on \(E\) can be approximated by this transformation with an arbitrary precision.

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Authors and Affiliations

  1. Department of Mathematics, Shiraz University of Technology, Modarres Blvd, 71555-313 , Shiraz, Iran

    S. Jahedi, M. J. Mehdipour & R. Rafizadeh

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  1. S. Jahedi
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  2. M. J. Mehdipour
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  3. R. Rafizadeh
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Correspondence to S. Jahedi.

Additional information

Communicated by T. Allahviranloo.

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Jahedi, S., Mehdipour, M.J. & Rafizadeh, R. Approximation of integrable functions based on \(\phi -\)transform. Soft Comput 18, 2015–2022 (2014). https://doi.org/10.1007/s00500-013-1182-8

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