On starlikeness of certain integral transforms

Let A denote the class of normalized analytic functions in the unit disc U = {z: |z| < 1}. The author obtains fixed values of δ and ϱ (δ ≈ 0.308390864..., ϱ ≈ 0.0903572...) such that the integral transforms F and G defined by ${\displaystyle F\left(z\right)={\int }_0^z\left(\frac{f\left(t\right)}{t}\right)dt}$ and ${\displaystyle G\left(z\right)=\left(\frac{2}{z}\right){\int }_0^{z}g\left(t\right)dt}$ are starlike (univalent) in U, whenever f ∈ A and g ∈ A satisfy Ref'(z) > -δ and Re g'(z) > -ϱ respectively in U.