TY - JOUR
AU - B. Chakraborty
PY - 2020/11/20
Y2 - 2020/11/29
TI - On the cardinality of a reduced unique range set
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 72
IS - 11
SE - Research articles
DO - 10.37863/umzh.v72i11.594
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/594
AB - UDC 517.5Two 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)).
ER -