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A new orthogonality and angle in a normed space

  • M. Nur
  • H. Gunawan
Article
  • 34 Downloads

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.

Keywords

\(g\!g\)-orthogonality \(g\!g\)-angle Normed spaces Strictly convex 

Mathematics Subject Classification

15A03 46B20 51N15 

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Notes

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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsHasanuddin UniversityMakassarIndonesia
  2. 2.Analysis and Geometry Group, Faculty of Mathematics and Natural SciencesBandung Institute of TechnologyBandungIndonesia

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