Some remarks on inequalities that characterize inner product spaces.
Orthogonality in normed linear spaces: A survey. Part II: Relations between main orthogonalities.
Orthogonality in normed linear spaces. A survey I: Main properties.
Weak moduli of convexity.
Let E be a real normed linear space with unit ball B and unit sphere S. The classical modulus of convexity of J. A. Clarkson [2] δE(ε) = inf {1 - 1/2||x + y||: x,y ∈ B, ||x - y|| ≥ ε} (0 ≤ ε ≤ 2) is well known and it is at the origin of a great number of moduli defined by several authors. Among them, D. F. Cudia [3] defined the directional, weak and directional weak modulus of convexity of E, respectively, as δE(ε,g)...
Metric ellipses in Minkowski planes.
An ellipse in R can be defined as the locus of points for which the sum of the Euclidean distances from the two foci is constant. In this paper we will look at the sets that are obtained by considering in the above definition distances induced by arbitrary norms.
Some characteristic and non-characteristic properties of inner product spaces
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