Abstract
We present a new orthogonality which is based on p-angular distance in normed linear spaces. This orthogonality generalizes the Singer and isosceles orthogonalities to a vast extent. Some important properties of this orthogonality, such as the \(\alpha \)-existence and the \(\alpha \)-diagonal existence, are established with giving some natural bounds for \(\alpha \). It is shown that a real normed linear space is an inner product space if and only if the p-angular distance orthogonality is either homogeneous or additive. Several examples are presented to illustrate the results.
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The authors would like to thank the referee for carefully reading the manuscript and for giving some helpful comments.
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Rooin, J., Rajabi, S. & Moslehian, M.S. p-angular distance orthogonality. Aequat. Math. 94, 103–121 (2020). https://doi.org/10.1007/s00010-019-00664-7
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DOI: https://doi.org/10.1007/s00010-019-00664-7