... 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 ... univalent in .Furthermore, by using the same techniques as in the proof of Theorem 3.1,wecanprovetheconvexity univalence of F and so the details may be omitted. Therefore, from Theorem 3 .3,we ... thatHp,q,sα1gzzp≺Hp,q,sα1fzzp.3.28Moreover, the function Hλ,q,sα1gz/zpis the best subordinant.10 Journal of Inequalities and ApplicationsProof. The first part of the proof is similar to that of Theorem 3.1 andsowewillusethesamenotation...