Operator Ky Fan type inequalities

In this paper, we extend some significant Ky Fan type inequalities in a large setting to operators on Hilbert spaces and derive their equality conditions. Among other things, we prove that if f:[0,∞)→[0,∞) is an operator monotone function with f(1)=1, f′(1)=μ, and associated mean σ, then for all operators A and B on a complex Hilbert space H such that 0