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A new orthogonality and angle in a normed space

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Abstract

We introduce the notion of \(g\!g\)-orthogonality in a normed space and discuss its basic properties. We also show the connection between \(g\!g\)-orthogonality and g-orthogonality introduced by Milic̀ic̀ (Mat Vesnik 39:325–334, 1987). Using \(g\!g\)-orthogonality, we introduce the notion of \(g\!g\)-angle between two vectors in a normed space and discuss its properties. Moreover, we apply the \(g\!g\)-angle to examine whether or not a normed space is strictly convex.

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Acknowledgements

The research is supported by ITB Research and Innovation Program 2018. The authors thank the referee for his/her useful comments and suggestions on the earlier version of this paper.

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  1. M. Nur & H. Gunawan

    Present address: Analysis and Geometry Group, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Jl. Ganesha 10, Bandung, 40132, Indonesia

Authors and Affiliations

  1. Department of Mathematics, Hasanuddin University, Jl. Perintis Kemerdekaan KM 10, Makassar, 90245, Indonesia

    M. Nur

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  1. M. Nur
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  2. H. Gunawan
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Correspondence to M. Nur.

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Nur, M., Gunawan, H. A new orthogonality and angle in a normed space. Aequat. Math. 93, 547–555 (2019). https://doi.org/10.1007/s00010-018-0582-3

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  • DOI: https://doi.org/10.1007/s00010-018-0582-3

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