On the Sharp Triangle Inequalities in Quasi-Banach Spaces

Abstract—The triangle inequality is one of the most important and fundamental inequalities in analysis. Many authors have been treating its generalizations and reverse inequalities. In this paper, we shall present the sharp triangle inequality and its reverse inequality for an arbitrary number of finitely many nonzero elements of a quasi-Banach space, which generalize the results obtained by C. Wu and Y. J. Li in [1]. Keywords-Triangle inequality; Sharp triangle inequality; Reverse inequality; Norm; Quasi-Banach space