In this short note, by using some of Chen’s theorems and classic analysis, we obtain a double inequality for triangle and give a positive answer to a problem posed by Yang and Yin [6].

In this paper we obtain some new Schwarz related inequalities in inner product spaces over the real or complex number field. Applications for the generalized triangle inequality are also given.

In this paper we obtain some new Schwarz related inequalities in inner product spaces over the real or complex number field. Applications for the generalized triangle inequality are also given.

We present an algorithm for the asymmetric traveling salesman problem on instances which satisfy the triangle inequality. Like several existing algorithms, it achieves approximation ratio O(log n). Unlike previous algorithms, it uses randomized rounding.

We consider the Asymmetric Traveling Salesman problem for costs satisfying the triangle inequality. We derive a randomized algorithm which delivers a solution within a factor O(log n/ log log n) of the optimum with high probability.

In this paper, the authors give a refinement of the inequality associated with the medians, inradius and circumradius in a triangle by making use of certain analytical techniques for systems of nonlinear algebraic equations.

Some additive reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.

In previous papers [1, 2], we proposed a subspace distance. However, whether the subspace distance satisfies the triangle inequality was left open. In this note, we give positive answer to the open problem and prove our assertion.

Determining molecular structure from interatomic distances is an important and challenging problem. Given a molecule with n atoms, lower and upper bounds on interatomic distances can usually be obtained only for a small subset of the n(n 1) 2 atom pairs, using NMR. Given the bounds so obtained on the distances between some of the atom pairs, it is often useful to compute tight bounds on all the...