In this paper we apply some elements of real analysis theory to the distinguishing of the certain subclass of the class of functions possessing Sharkovsky property. The main aim of this is connected with the answer to the following question: what kind of assumption should we impose on Sharkovsky function $f$ in order to have that there exists a ring of functions possessing Sharkovsky property containing $f$?
"First-Return Limiting Notions and Rings of Sharkovsky Functions." Real Anal. Exchange 34 (2) 549 - 564, 2008/2009.