Geodesic
On Approximate Birkhoff-James Orthogonality and Normal Cones in a Normed Space
Journal of convex analysis, Tome 26 (2019) no. 1, pp. 341-351
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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.
Classification : 46B20, 52A10
Mots-clés : Approximate Birkhoff-James orthogonality, normal cones 
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     author = {D. Sain and K. Paul and A. Mal},
     title = {On {Approximate} {Birkhoff-James} {Orthogonality} and {Normal} {Cones} in a {Normed} {Space}},
     journal = {Journal of convex analysis},
     pages = {341--351},
     year = {2019},
     volume = {26},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2019_26_1_JCA_2019_26_1_a18/}
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D. Sain; K. Paul; A. Mal. On Approximate Birkhoff-James Orthogonality and Normal Cones in a Normed Space. Journal of convex analysis, Tome 26 (2019) no. 1, pp. 341-351. http://geodesic.mathdoc.fr/item/JCA_2019_26_1_JCA_2019_26_1_a18/