Argument Property for Certain Analytic Functions
نویسندگان
چکیده
and Applied Analysis 3 2. Main Result Our main theorem is given by the following. Theorem 2.1. Let λ0 > 0, 0 < a ≤ 1 max{α1, α2} , |b 1| ≤ 2 α1 α2 , 0 ≤ a − b − 1 ≤ 1 max{α1, α2} . 2.1 If p ∈ P satisfies −2 2 < arg ( λ0 ( p z )a zp′ z ( p z )b ) < γ1π 2 z ∈ U , 2.2 where γj γj a, b, α1, α2 aαj 2 π tan−1 ( α1 α2 /2 cos ( βπ/2 ) cos ( a − b − 1 αjπ/2 ) 2λ0δj a, b, α1, α2 α1 α2 /2 cos ( βπ/2 ) sin ( a − b − 1 αjπ/2 ) ) ( j 1, 2 ) , δj a, b, α1, α2 [( 1 − ( A cosβπ/22 )1/2 −1 j sinβπ/2 ]1 A 2 [ 1 − A cosβπ/22 −1 j ( 1 − ( A cosβπ/22 )1/2 sin ( βπ/2 ) ]A ( j 1, 2 ) ,
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