On sharp triangle inequalities in Banach spaces

Abstract

We shall present a couple of norm inequalities which will much improve the sharp triangle inequality with n elements and its reverse inequality in a Banach space shown recently by the last three authors.

Another approach to characterizations of generalized triangle inequalities in normed spaces

“…Let ( Forψ ∈Ψ , we define · ψ as in (8), and consider (X · ψ ) which is denoted by ψ (X ). Note that ψ (X ) is not a normed space.…”

“…[1,4,5,7,8]). In this paper, for a normed linear space (X · ), we consider the following generalized triangle inequality which is involved with the…”

Characterization of intermediate values of the triangle inequality II

“…In [8] and [13] two results on intermediate values of the triangle inequality were presented. They were generalized in [11] with a result which characterizes all intermediate values of the triangle inequality.…”

On Sharp Triangle Inequalities in Banach Spaces II

“…

Sharp triangle inequality and its reverse in Banach spaces were recently showed by Mitani et al 2007 . In this paper, we present equality attainedness for these inequalities in strictly convex Banach spaces.

…”