Journal of Convex Analysis 26 (2019), No. 1, 341--351
Copyright Heldermann Verlag 2019
On Approximate Birkhoff-James Orthogonality and Normal Cones in a Normed Space
Debmalya Sain
Dept. of Mathematics, Indian Institute of Science, Bengaluru 560012, Karnataka -- India
saindebmalya@gmail.com
Kallol Paul
Dept. of Mathematics, Jadavpur University, Kolkata 700032, West Bengal -- India
kalloldada@gmail.com
Arpita Mal
Dept. of Mathematics, Jadavpur University, Kolkata 700032, West Bengal -- India
arpitamalju@gmail.com
We study two notions of approximate Birkhoff-James orthogonality in a normed space, from a geometric point of view, and characterize them in terms of normal cones. We further explore the interconnection between normal cones and approximate Birkhoff-James orthogonality to obtain a complete characterization of normal cones in a two-dimensional smooth Banach space. We also obtain a uniqueness theorem for approximate Birkhoff-James orthogonality set in a normed space.
Keywords: Approximate Birkhoff-James orthogonality, normal cones.
MSC: 46B20; 52A10
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