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.
Abstract. Let S denote the family of functions f, holomorphic and univalent in the open unit disk U, and normalized by f(0) = 0, f'(0) = 1.