Argument inequalities 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 Inequalities for Certain Analytic Functions

Certain Inequalities for Classes of Analytic Functions with Varying Argument of Coefficients

In this paper we introduce new classes of analytic functions with varying argument of coefficients defined by subordination. Several properties like the coefficients inequalities, distortion bounds, subordination theorems and integral means inequalities are investigated. Some consequences of our main results for new or well-known classes of functions are also pointed out. Mathematics subject cl...

Certain Inequalities for a General Class of Analytic and Bi-univalent Functions

In this work, the subclass of the function class S of analytic and bi-univalent functions is defined and studied in the open unit disc. Estimates for initial coefficients of Taylor- Maclaurin series of bi-univalent functions belonging these class are obtained. By choosing the special values for parameters and functions it is shown that the class reduces to several earlier known classes of analy...

Coefficient Inequalities for Certain Classes of Analytic and Univalent Functions

For functions f(z) which are starlike of order α, convex of order α, and λ-spirallike of order α in the open unit disk U, some interesting sufficient conditions involving coefficient inequalities for f(z) are discussed. Several (known or new) special cases and consequences of these coefficient inequalities are also considered.