Argument and Coefficient Estimates for Certain Analytic Functions

Argument Property for Certain Analytic Functions

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...

Coefficient estimates for a subclass of analytic and bi-univalent functions

In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk. Upper bounds for the second and third coefficients of functions in this subclass are founded. Our results, which are presented in this paper, generalize and improve those in related works of several earlier authors.

Coefficient Estimates for Some Subclasses of Analytic and Bi-Univalent Functions Associated with Conic Domain

The main objective of this investigation is to introduce certain new subclasses of the class $Sigma $ of bi-univalent functions by using concept of conic domain. Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients $ left vert a_{2}right vert $ and $left vert a_{3}right vert $ for functions in these new subclasses. We consider various corollaries and consequen...

Coefficient Inequalities for Certain Analytic Functions

Coefficient estimates for a certain subclass of analytic and bi-univalent functions

For λ ≥ 0 and 0 ≤ α < 1 < β, we denote by K (λ;α, β) the class of normalized analytic functions satisfying the two sided-inequality α << ( z f ′(z) f (z) + λ z2 f ′′(z) f (z) ) < β (z ∈ U), where U is the open unit disk. Let KΣ(λ;α, β) be the class of bi-univalent functions such that f and its inverse f −1 both belong to the class K (λ;α, β). In this paper, we establish bounds for the coefficie...