On the cardinality of a reduced unique range set
Abstract
UDC 517.5
Two meromorphic functions are said to share a set $S\subset \mathbb{C}\cup\{\infty\}$ ignoring multiplicities (IM) if $S$ has the same pre-images under both functions.
If any two nonconstant meromorphic functions, sharing a set IM, are identical, then the set is called a “reduced unique range set for meromorphic functions'' (in short, RURSM or URSM-IM).
From the existing literature, it is known that there exists a RURSM with seventeen elements. In this article, we reduced the cardinality of an existing RURSM and established that there exists a RURSM with fifteen elements. Our result gives an affirmative answer to the question of L. Z. Yang
(Int. Soc. Anal., Appl., and Comput., 7, 551–564 (2000)).
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Copyright (c) 2020 B. Chakraborty
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