On the existence of unique range sets generated by non-critically injective polynomials and related issues
S. Mallick
In this paper, we prove the existence of non-critically injective polynomials whose set of zeros form unique range sets that answers one of the most awaited and
fundamental questions of uniqueness theory of entire and meromorphic functions. We also show that there exist some unique range sets and their generating polynomials
which can not be characterized by any of the existing generalized results of unique range sets
but as an application of our main theorems the same can be characterized. Moreover, as an application of our main results we prove that the cardinality of a unique
range set does not always depend upon the number of distinct critical points of its generating polynomial.
Tbilisi Mathematical Journal, Vol. 13(4) (2020), pp. 81-101
|