On Coefficient Estimates and Conjectures for the Class ... .
Some inequalities are proved for coefficients of functions in the class P(α), where α ∈ [0,1), of functions with real part greater than α. In particular, new inequalities for coefficients in the Carathéodory class P(0) are given.
We prove that each degree two quasiregular polynomial is conjugate to Q(z) = z² - (p+q)|z|² + pqz̅² + c, |p| < 1, |q| < 1. We also show that the complexification of Q can be extended to a polynomial endomorphism of ℂℙ² which acts as a Blaschke product (z-p)/(1-p̅z) · (z-q)/(1-q̅z) on ℂℙ²∖ℂ². Using this fact we study the dynamics of Q under iteration.
We give several definitions of the pluricomplex Green function and show their equivalence.
In this paper, we obtain some applications of first order differential subordination and superordination results involving certain linear operator and other linear operators for certain normalized analytic functions. Some of our results improve and generalize previously known results.