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Bornological Coderivative and Subdifferential Calculus in Smooth Banach Spaces

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Abstract

In this paper, we study bornological generalized differential properties of sets with nonsmooth boundaries, nonsmooth functions, and set-valued mappings in smooth Banach spaces. We establish a fuzzy intersection rule for bornological normal cones and develop fuzzy calculus for bornological generalized differential constructions as well as exact calculus for the limiting counterparts of these constructions.

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Acknowledgements

We are grateful to anonymous referees for their valuable suggestions and remarks that allowed us to improve the original presentation.

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Authors and Affiliations

  1. Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Oregon, OR, 97201, USA

    Nguyen Mau Nam

  2. Department of Mathematical Sciences, University of Massachusetts Lowell, Lowell, MA, 01854, USA

    Hung M. Phan

  3. Department of Mathematics and Statistics, Eastern Michigan University, Ypsilanti, MI, 48197, USA

    Bingwu Wang

Authors
  1. Nguyen Mau Nam
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  2. Hung M. Phan
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  3. Bingwu Wang
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Correspondence to Nguyen Mau Nam.

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Dedicated to Boris S. Mordukhovich on the occasion of his 70th birthday

Research of Nguyen Mau Nam was partly supported by the National Science Foundation under grant DMS-1716057. Hung M. Phan was partly supported by Autodesk Inc. via a gift made to the Department of Mathematical Sciences, University of Massachusetts Lowell.

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Nam, N.M., Phan, H.M. & Wang, B. Bornological Coderivative and Subdifferential Calculus in Smooth Banach Spaces. Set-Valued Var. Anal 27, 971–993 (2019). https://doi.org/10.1007/s11228-018-0503-6

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  • DOI: https://doi.org/10.1007/s11228-018-0503-6

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