A new orthogonality and angle in a normed space
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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 Classification15A03 46B20 51N15
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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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