id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-540	Aouf, Mohamed Kamal; Seoudy, Tamer M.	Differential Sandwich Theorems of Analytic Functions Defined by Linear Operators	2011	13	.pdf	application/pdf	5170	334	82	If f , g ∈A satisfy the following subordination condition: � 1+ γ λ � zDn+1 λ ( f ∗ g)(z) � Dn λ ( f ∗ g)(z) �2 + γ λ    zDn+2 λ ( f ∗ g)(z) � Dn λ ( f ∗ g)(z) �2 − 2 z � Dn+1 λ ( f ∗ g)(z) �2 � Dn λ ( f ∗ g)(z) �3    ≺ q (z) + γzq ′ (z) , (16) then zDn+1 λ ( f ∗ g)(z) � Dn λ ( f ∗ g)(z) �2 ≺ q (z) and q (z) is the best dominant. Therefore, differentiating (17) logarith- mically with respect to z and using the identity (8) in the resulting equation, we have � 1+ γ λ � zDn+1 λ ( f ∗ g)(z) � Dn λ ( f ∗ g)(z) �2 + γ λ    zDn+2 λ ( f ∗ g)(z) � Dn λ ( f ∗ g)(z) �2 − 2 z � Dn+1 λ ( f ∗ g)(z) �2 � Dn λ ( f ∗ g)(z) �3    = p (z)+γzp ′ (z) , that is, p (z) + γzp ′ (z) ≺ q (z) + γzq ′ (z) .	cache/ejpam-540.pdf	txt/ejpam-540.txt