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...

This paper utilizes the method of extremal length to study several diameter problems for functions conformal outside of a disc centered at the origin, with a standard normalization, which possess a quasiconformal extension to a ring subdomain of this disc. Known results on the diameter of a complementary component of the image domain of a univalent function are extended. Applications to the tra...

Abstract In this article, it is shown that Koebe inner functions and squares of singular Nevanlinna functions, so called atomic density have minimal realizations in reproducing kernel Krein spaces.

A variant of the Circle Packing Theorem states that combinatorial class any convex polyhedron contains elements, called Koebe polyhedra, midscribed to unit sphere centered at origin, and these representatives are unique up Mobius transformations sphere. Motivated by this result, various papers investigate problem centering spherical configurations under transformations. In particular, Springbor...

The Koebe One Quarter Theorem states that the range of any Schlicht function contains centered disc radius 1/4 which is sharp due to value at −1. A natural question finding polynomials set sharpness for polynomials. In particular, it was asked in [7] whether Suffridge [15] are optimal. For degree 1 and 2 obviously true. It demonstrated [10] 3 not optimal a promising alternative family introduce...