Angles, triangle inequalities, correlation matrices and   metric-preserving and subadditive functions
  We study the triangle inequalities for angles (with different definitions) and present inequalities concerning the entries of correlation matrices through the positivity of $3\times 3$ matrices. We extend our discussions to the inequalities concerning the triangle triplets with metric-preserving and subadditive functions. 
Diego Castano, Vehbi E. Paksoy, and Fuzhen Zhang
math.FA