title: Improved estimates for the triangle inequality.
abstract: We obtain refined estimates of the triangle inequality in a normed space using integrals and the Tapia semi-product. The particular case of an inner product space is discussed in more detail.
authors.affiliation: Faculty of Mathematics and Computer Science, Transilvania University of Braşov, Str. Iuliu Maniu, nr. 50, Braşov, 500091 Romania.
authors.forename: Nicuşor
authors.initials: N
authors.lastname: Minculete
authors.affiliation: Faculty of Mathematics and Computer Science, Transilvania University of Braşov, Str. Iuliu Maniu, nr. 50, Braşov, 500091 Romania.
authors.forename: Radu
authors.initials: R
authors.lastname: Păltănea
keywords: Tapia semi-product; inner product spaces; norm inequalities; norm-angular distance; triangle inequality