Some starlikeness criterions for analytic functions.
For α ∈ [0,1] and β ∈ (-π/2,π/2) we introduce the classes defined as follows: a function f regular in U = z: |z| < 1 of the form , z ∈ U, belongs to the class if for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in are examined.
The authors introduce two new subclasses and of meromorphically multivalent functions. Distortion bounds and convolution properties for , and their subclasses with positive coefficients are obtained. Some inclusion relations for these function classes are also given.
We discuss the uniqueness of meromorphic functions when they share three sets with the notion of weighted sharing and improve two results of Lahiri-Banerjee and Yi-Lin. We also improve a recent result of the present author and thus provide an answer to a question of Gross, in a new direction.