Bornological Coderivative and Subdifferential Calculus in Smooth Banach Spaces

  • Nguyen Mau NamEmail author
  • Hung M. Phan
  • Bingwu Wang


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.


Bornology Generalized differentiation Bornological subdifferential Bornological normal cone Bornological coderivative 

Mathematics Subject Classifications (2010)

Primary 49J52, 49J53 Secondary 90C30 


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


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Fariborz Maseeh Department of Mathematics and StatisticsPortland State UniversityOregonUSA
  2. 2.Department of Mathematical SciencesUniversity of Massachusetts LowellLowellUSA
  3. 3.Department of Mathematics and StatisticsEastern Michigan UniversityYpsilantiUSA

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