Radially distributed values and normal families, II

TL;DR

This paper investigates the normality of families of holomorphic functions in the unit disk with zeros and 1-points constrained to specific rays, extending understanding of value distribution and normality criteria.

Contribution

It establishes conditions under which such families are normal outside the origin for particular ray configurations.

Findings

Family is normal outside the origin for certain ray arrangements.

Zeros and 1-points constrained to rays influence normality.

Extends previous results on value distribution and normal families.

Abstract

We consider the family of all functions holomorphic in the unit disk for which the zeros lie on one ray while the 1-points lie on two different rays. We prove that for certain configurations of the rays this family is normal outside the origin.