Journal of Convex Analysis 29 (2022), No. 3, 731--747
Copyright Heldermann Verlag 2022
Best Approximative Properties of Exposed Faces
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
Let X = c01(μ). 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.
Keywords: Proximinal, strongly proximinal, norm attaining functional, exposed face, Hausdorff metric continuity.
MSC: 46B20, 41A50, 41A65.
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