On some analogue of the shah equation for analytic in the unit disk functions

Анотація

For a function of the form f (z) = F (1/(1 − z)), analytic in the unit disk, where F is an entire transcendental function, satisfying the differential equation ${(1-z)}^{4}w\text{'}\text{'}+({\xi }_1{(1-z)}^3+{\xi }_0{(1-z)}^2)w\text{'}+({\psi }_2{(1-z)}^2+{\psi }_1(1-z)+{\psi }_0)w=0$,

the boundedness of the l-index, starlikeness, convexity, close-to-convexity and growth are investigated.