Abstract

Let X = c0c_0 or L1(μ)L_1(\mu). We will show that the exposed face of the unit sphere of X is strongly proximinal and the corresponding metric projection map is Hausdorff metric continuous.

Author information

Contact details are reproduced from the original publication and may be historical.

N. Prakash

Dept. of Mathematics, National Institute of Technology Tiruchirappalli, Trichy, Tamil Nadu, India

prakashn@nitt.edu

K. V. Sangeetha

Dept. of Mathematics, National Institute of Technology Tiruchirappalli, Trichy, Tamil Nadu, India

sangeekv@gmail.com

Keywords

  • Proximinal
  • strongly proximinal
  • norm attaining functional
  • exposed face
  • Hausdorff metric continuity

Mathematics Subject Classification

46B20, 41A50, 41A65

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Suggested citation

N. Prakash, K. V. Sangeetha. “Best Approximative Properties of Exposed Faces.” Journal of Convex Analysis 29 (2022), No. 3, 731–747. https://doi.org/10.68381/jca29041

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Published by Heldermann Verlag, 2022. Rights now held by Banach Press LLC.