On Several Bounds for Types of Angular Distances

Augusta Raţiu () and Nicuşor Minculete
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Augusta Raţiu: Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, 550012 Sibiu, Romania
Nicuşor Minculete: Department of Mathematics and Computer Science, Transilvania University of Braşov, 500091 Braşov, Romania

Mathematics, 2022, vol. 10, issue 18, 1-10

Abstract: In this study, we introduce the expression d λ ( x , y ) : = λ ∥ x ∥ + ( 1 − λ ) ∥ y ∥ − ∥ λ x + ( 1 − λ ) y ∥ on the real normed space X ( X , ∥ · ∥ ) , where x , y ∈ X and λ ∈ R . We characterize this expression and find various estimates of it. We also obtain a generalization and some refinements of Maligranda’s inequality. Finally, we give some relations between d λ ( x , y ) and several types of angular distances between two nonzero vectors in a real normed space.

Keywords: normed space; triangle inequality; Maligranda inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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