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Comments on a selector theorem in Banach spaces

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Abstract

Recently, Cole (Ref. 1) presented a selection theorem in reflexive Banach spaces under certain convexity assumptions. In this paper, we present a proof of Cole's selection theorem without imposing the convexity condition. This makes the result more powerful for application in optimal control theory.

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References

  1. Cole, J. K.,A Selector Theorem on Banach Spaces, Journal of Optimization Theory and Applications, Vol. 7, No. 3, 1971.

  2. Cesari, L.,Existence Theorem for Multidimensional Lagrange Problems, Journal of Optimization Theory and Applications, Vol. 1, No. 2, 1967.

  3. Dunford, N., andSchwartz, J. T.,Linear Operators, Part 1, John Wiley and Sons (Interscience Publishers), p. 430, New York, New York, 1964.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Ottawa, Ottawa, Canada

    N. U. Ahmed (Associated Professor)

  2. Department of Applied Mathematics, University of New South Wales, New South Wales, Australia

    K. L. Teo (Lecturer)

Authors
  1. N. U. Ahmed
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  2. K. L. Teo
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Additional information

Communicated by L. Cesari

The authors would like to thank Professor L. Cesari for pointing out a critical misprint in the original version of this note.

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Ahmed, N.U., Teo, K.L. Comments on a selector theorem in Banach spaces. J Optim Theory Appl 19, 117–118 (1976). https://doi.org/10.1007/BF00934055

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  • DOI: https://doi.org/10.1007/BF00934055

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