On some metric inequalities and applications (Q2211419)

Summary: We derive a new inequality in metric spaces and provide its geometric interpretation. Some applications of our result are given, including metric inequalities in Lebesgue spaces, matrices inequalities, multiplicative metric inequalities, and partial metric inequalities. Our main result is a generalization of that obtained by \textit{S. S. Dragomir} and \textit{A. C. Goşa} [J. Indones. Math. Soc. 11, No. 1, 33--38 (2005; Zbl 1069.54507)].