operator Jensen's inequality, operator monotone, operator mean
Refinements of the operator Jensen's inequality for convex and operator convex functions are given by using cyclic refinements of the discrete Jensen's inequality. Similar refinements are fairly rare in the literature. Some applications of the results to norm inequalities, the Holder McCarthy inequality and generalized weighted power means for operators are presented.
Horvath, Laszlo; Khan, Khuram A.; and Pecaric, Josip.
"Cyclic Refinements of the Different Versions of Operator Jensen's Inequality",
Electronic Journal of Linear Algebra,
Volume 31, pp. 125-133.