Triangle inequalities in inner-product spaces


  • Martin Lukarevski
  • Dan Stefan Marinescu



Inner-product space, Tereshin's inequality, Panaitopol's inequality


Tereshin's and Panaitopol's are known inequalities involving the median, circumradius and sides of the triangle. In this short note we generalize the inequalities to inner-product spaces. As an application we derive inequality for the median and the radius of the circumscribed sphere of an $n$-dimensional simplex.


R. Bellman, Why study inequalities? in General Inequalities 2, Springer (1980)

M. S. Klamkin, A. Meir, Ptolemy's inequality, chordal metric, multiplicative metric, Pac. J. Math. 101, No. 2, (1982), pp. 389-392

D. S. Marinescu, V. Cornea, Inegalitati pentru mediane, bimediane, bisectoare, Recreatii Matematica 2, (2003) pp. 5-8

D. S. Marinescu, M. Monea. M. Opincariu, M. Stroe, Some equivalent characterizations of inner product spaces and their consequences, Filomat 29, No. 7, (2015) pp. 1587-1599

D. S. Marinescu, M. Monea, A proof of Garfunkel inequality and of some related results in inner-product spaces, Creat. Math. Inform. Vol. 26, No. 2 (2017), pp. 153-162

I. J. Schoenberg, A remark on M. M. Day's characterization of inner-product spaces and a conjecture of L. M. Blumenthal, Proc. Amer. Soc. 3 (1952) pp. 961-964

G. Tsintsifas, Problem E 2471, Amer. Math. Monthly 81 (1974), 82 (1975) pp. 523-524




How to Cite

Lukarevski, M. ., & Marinescu, D. S. (2022). Triangle inequalities in inner-product spaces. Innovative Journal of Mathematics (IJM), 1(2), 14–17.