SUT J. Math. 56 (2), 109-127, (December 2020) DOI: 10.55937/sut/1609966712
KEYWORDS: operator convex functions, integral inequalities, Hermite-Hadamard inequality, Féjer’s inequalities, 47A63, 47A99
Let be an operator convex function on and the convex set of selfadjoint operators with spectra in . If and , as an operator function, is Gâteaux differentiable on
while is Lebesgue integrable satisfying the condition
and symmetric, namely for all then
Some particular examples of interest are also given.