Corresponding to the concept of p-angular distance α p [x, y] := x p−1 x − y p−1 y , we first introduce the notion of skew p-angular distance β p [x, y] := y p−1 x − x p−1 y for non-zero elements of x, y in a real normed linear space and study some of significant geometric properties of the p-angular and the skew p-angular distances. We then give some results comparing two different p-angular distances with each other. Finally, we present some characterizations of inner product spaces related to the p-angular and the skew p-angular distances. In particular, we show that if p > 1 is a real number, then a real normed space X is an inner product space, if and only if for any2010 Mathematics Subject Classification. 46B20, 46C15, 26D15.
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