| Abstract: | A triple (x, y, z) in a linear 2-normed space (X, ‖.,.‖) is called an isosceles orthogonal triple, denoted |(x, y, z), if  |(.,.,.) is said to be homogeneous if |(x, y, z) implies |(ax, y, z) for all real a and it is additive if |(x1, y, z) and |(x2, y, z) imply that |(x1 + x2, y, z). In addition to developing some basic properties of |(.,.,.), this paper shows that under the assumption of strict convexity, every subspace of X of dimension ≤ 3 contains an isosceles orthogonal triple. Further, if (X, ‖.,.‖) is strictly convex and |(…,.) is either homogeneous or additive, then (X, ‖.,.‖) is a 2-inner product space. |
