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Orthogonality connected with integral means and characterizations of inner product spaces

Abstract

Kikianty and Dragomir (Math Inequal Appl 13:1–32, 2010) introduced the pHH norms on the Cartesian square of a normed space, which are equivalent, but are geometrically different, to the well-known p-norms. In this paper, notions of orthogonality in terms of the 2−HH norm are introduced; and their properties are studied. Some characterizations of inner product spaces are established, as well as a characterization of strictly convex spaces.

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Correspondence to Eder Kikianty.

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Dragomir, S.S., Kikianty, E. Orthogonality connected with integral means and characterizations of inner product spaces. J. Geom. 98, 33–49 (2010). https://doi.org/10.1007/s00022-010-0048-9

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Mathematics Subject Classification (2010)

  • 46B20
  • 46C05

Keywords

  • Orthogonality
  • Pythagorean orthogonality
  • Isosceles orthogonality
  • inner product space
  • strictly convex space
  • Cartesian product space