On the Koebe Quarter Theorem for certain polynomials

Certain Conditions for Starlikeness of Analytic Functions of Koebe Type

For α ≥ 0, λ > 0, we consider theM α, λ b of normalized analytic α−λ convex functions defined in the open unit disc U. In this paper, we investigate the classM α, λ b, that is, Re{ zf ′ b z /fb z 1− α α 1 − λ zf ′ b z /fb z αλ 1 zf ′′ b z /f ′ b z } > 0, with fb is Koebe type, that is, fb z : z/ 1−zn . The subordination result for the aforementioned class will be given. Further, bymaking use of...

Note on a Theorem of Bôcher and Koebe*

Note on Certain Orthogonal Polynomials

On the average number of sharp crossings of certain Gaussian random polynomials

A Theorem on Difference Polynomials

We shall prove the following analogue of a theorem of Kronecker's : Let J be a difference field containing an element t which is distinct from its transforms of any order. Every perfect ideal in the ring 7\yu ' ' ' y y<n\ has a basis consisting of n + 1 difference polynomials. The corresponding theorem for differential polynomials was proved by J. F. Ritt. We shall follow in all but details a b...