We prove the case ρ=1/4 of the following conjecture of Koumandos and Ruscheweyh: let snμ(z)=Σk=0n(μ)k/ k!zk, and for ρε(0,1] let μ≤(ρ) be the unique solution of 0(ρ+1)πsin(t-ρπ)tμ-1dt =0 in (0,1]. Then we have pipearg[(1 ...

We completely determine the set of (α, β) ∈ ℝ2for which the function is convex on (0, ∞) and use this result to give some special classes of completely monotonic functions of positive order related to gamma and psi functions. ...