General Univalence Criterion Associated with thenth Derivative

Univalence Criterion for Analytic Functions

In this paper, we obtain a new univalence criterion for analytic functions defined outside of the unit disk. Relevant connections of the results, which are presented in this paper with various known results are also considered. 2000 Mathematics Subject Classification: Primary 30C45.

Univalence of a New General Integral Operator Associated with the q-Hypergeometric Function

Univalence criteria for general integral operator

Let A be the class of all analytic functions which are analytic in the open unit disc U = {z : |z| < 1} and Gb = { f ∈ A : ∣∣∣∣ 1 + zf ′′(z)/f ′(z) zf ′(z)/f(z) − 1 ∣∣∣∣ < b, z ∈ U } . In this paper, we derive sufficient conditions for the integral operator Ii γ (f1, ..., fn)(z) =    z ∫ 0 tγ−1 ( f ′ 1(t) )α1 ( f1(t) t )1−α1 ... ( f ′ n(t) )αn ( fn(t) t )1−αn dt    1 γ to be analytic and ...

Univalence conditions for a general integral operator

For analytic functions in the open unit disk U , we define a new general integral operator. The main object of the this paper is to study this new integral operator and to determine univalence conditions of it. Several corollaries of the main results are also considered.

Univalence Criteria for a General Integral Operator

In this paper the author introduces a general integral operator and determines conditions for the univalence of this integral operator. Also, the significant relationships and relevance with other results are also given.