We show some estimates for the logarithmic mean that are obtained from operator inequalities between the Barbour path and the Heinz means.

In this paper, we present various functional means in the sense of convex analysis. In particular, a logarithmic mean involving convex functionals, extending the scalar one, is introduced. In the quadratic case, our functional approach implies immediately that of positive operators. Some examples, illustrating theoretical results and showing the interest of our functional approach, are discussed.

The purpose of this paper is to introduce the weighted logarithmic mean two accretive matrices. Among obtained results, we present some inequalities about when involved matrices are sectorial Our approach allowed us derive a new matrix which connected Heinz mean.

To calculate the driving temperature difference between hot and cold side of a heat exchanger, use logarithmic mean is common practice. provide high robustness in complex dynamic system models, robust formulation (logmean) function becomes vital. As analytic definition logmean naturally comes along with singularities limitations for specific input conditions, it essential to extend modify excha...