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.
In this paper we consider non-normalized univalent subordination chains and the connection with the Loewner differential equation on the unit ball in . To this end, we study the most general form of the initial value problem for the transition mapping, and prove the existence and uniqueness of solutions. Also we introduce the notion of generalized spirallikeness with respect to a measurable matrix-valued mapping, and investigate this notion from the point of view of non-normalized univalent subordination...
We investigate the starlike, convex and close-to-convex functions of complex order involving generalized multiplier transformations by means of the Hadamard product.