id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-856	Selvaraj, C.; Selvakumaran, K. A.	Majorization for Certain Classes of Analytic Functions Defined by a Generalized Operator	2010	7	.pdf	application/pdf	2522	135	85	If � D p,m λ (α1,β1) f (z) �( j) is majorized by � D p,m λ (α1,β1)g(z) �( j) in U for j ∈ N0, then � � � D p,m+1 λ (α1,β1) f (z) �( j) � � ≤ � � � D p,m+1 λ (α1,β1)g(z) �( j) � � for |z| ≤ r1, (9) where r1 = r1(p,γ,λ,A, B) is the smallest positive root of the equation |γλ(A− B) + pB|r3 − (p+ 2λ|B|)r2− (|γλ(A− B) + pB|+ 2λ)r + p = 0 (10) (−1≤ B < A≤ 1; p ∈ N; γ ∈ C− {0}; λ≥ 0). A function f (z) ∈ Ap is said to be in the class S p, j λ,m(A, B;γ) of p-valent functions of complex order γ 6= 0 in U if and only if Re � 1+ 1 γ � z � D p,m λ (α1,β1) f (z) �( j+1) � D p,m λ (α1,β1	cache/ejpam-856.pdf	txt/ejpam-856.txt