2024/06/19 by Dash, Prachi Prajna, Prajapat, Jugal Kishore
#30C45 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2406.13298
For the family of analytic functions f(z) in the open unit disk \mathbbD with f(0)=f'(0)-1=0, satisfying the differential equation zf'(z) - f(z) = \dfrac12 z2 ϕ(z), |ϕ(z)| ≤ 1, we obtain radii of convexity, starlikeness, and close-to-convexity of partial sums of f(z). We also study the generalization of this family having the form zf'(z)-f(z) = λz2 ϕ(z), |ϕ(z)| ≤ 1, where λ> 0, and obtain some useful properties of these functions.