Some inequalities related to triangle inequality

We deal with three well-known inequalities in normed spaces concerning the triangle inequality. The first is about (p,q)-angular distance which is a generalization of the notion of angular distance and p-angular distance discussed in the literature. The second relates to the Cauchy-Schowarz inequality. Finally, we introduce a norm in an inner product space through a given linear operator T and then we state a refinement of triangle inequality via the original norm of the space.

کلیدواژه ها:

Dunkle–Williams inequality ، Cauchy-Schowarz inequality ، triangle in- equality ، (p ، q)-angular distance