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On Several Bounds for Types of Angular Distances

Author

Listed:
  • Augusta Raţiu

    (Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, 550012 Sibiu, Romania
    These authors contributed equally to this work.)

  • Nicuşor Minculete

    (Department of Mathematics and Computer Science, Transilvania University of Braşov, 500091 Braşov, Romania
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Augusta Raţiu & Nicuşor Minculete, 2022. "On Several Bounds for Types of Angular Distances," Mathematics, MDPI, vol. 10(18), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3303-:d:912652
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    References listed on IDEAS

    as
    1. Nicuşor Minculete & Hamid Reza Moradi, 2020. "Some Improvements of the Cauchy-Schwarz Inequality Using the Tapia Semi-Inner-Product," Mathematics, MDPI, vol. 8(12), pages 1-13, November.
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