Uniformly convex Banach spaces are reflexive–-constructively. Bridges, D. S., Ishihara, H., & McKubre-Jordens, M. MLQ Math. Log. Q., 59(4-5):352–356, 2013.
Uniformly convex Banach spaces are reflexive–-constructively [link]Paper  doi  bibtex   
@ARTICLE{BIM13,
  author = {Bridges, Douglas S. and Ishihara, Hajime and McKubre-Jordens, Maarten},
  title = {Uniformly convex {B}anach spaces are reflexive---constructively},
  journal = {MLQ Math. Log. Q.},
  year = {2013},
  volume = {59},
  pages = {352--356},
  number = {4-5},
  doi = {10.1002/malq.201200093},
  fjournal = {MLQ. Mathematical Logic Quarterly},
  issn = {0942-5616},
  keywords = {bib, cca, con},
  mrclass = {46S30 (03F65 46B20)},
  mrnumber = {3100759},
  mrreviewer = {Lumini{\c{t}}a Simona V{\^{\i}}{\c{t}}{\u{a}}},
  owner = {Vasco},
  timestamp = {2015.10.01},
  url = {http://dx.doi.org/10.1002/malq.201200093}
}

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