Orthogonality connected with integral means and characterizations of inner product spaces

Kikianty and Dragomir (Math Inequal Appl 13:1–32, 2010) introduced the p?HH 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.