... M. Ali, V. Ravichandran, and N. Seenivasagan, On subordination and superordination of the multiplier transformation for meromorphic functions,” Bulletin of the Malaysian Mathematical SciencesSociety, ... part of the proof is similar to that of Theorem 3.3 a combined proof of Theorems 3.1 and 3.2 and is therefore omitted.By using the same methods as in the proof of Corollary 3.4, the following ... virtue of subordination condition 3.4. This contradicts the above observation thatLζ0,t /∈ ϕ . Therefore, subordination condition 3.4 must imply the subordination givenby 3.16.ConsideringFzGz,...