Non-commutative Callebaut inequality
  We present an operator version of the Callebaut inequality involving the interpolation paths and apply it to the weighted operator geometric means. We also establish a matrix version of the Callebaut inequality and as a consequence obtain an inequality including the Hadamard product of matrices. 
M. S. Moslehian, J. S. Matharu, J. S. Aujla
math.FA math.OA