On new classes of analytic functions with negative coefficients.
In the present paper, we obtain coefficient estimates for new subclass of analytic functions with respect to symmetric points. A sufficient condition for a function to belong to this class of function is also obtained.
We deal with functions given by the formula where are starlike of order and are complex constants. In particular, radii of starlikeness and convexity as well as orders of starlikeness and convexity are found.
We construct bounded domains D not equal to a ball in n ≥ 3 dimensional Euclidean space, Rn, for which ∂D is homeomorphic to a sphere under a quasiconformal mapping of Rn and such that n - 1 dimensional Hausdorff measure equals harmonic measure on ∂D.