Taking the question posed by the first author in [1] into background, we
further exhaust-ably investigate existing Fujimoto type Strong Uniqueness
Polynomial for Meromorphic functions (SUPM). We also introduce a new kind of
SUPM named Restricted SUPM and exhibit some results which will give us a new
direction to discuss the characteristics of a SUPM. Moreover, throughout the
paper, we pose a number of open questions for future research.
Boundedness properties of the operators of best approximation by analytic and meromorphic functions