SUBCLASSES OF MEROMORPHICALLY P-VALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS ASSOCIATED WITH A LINEAR OPERATOR
The aim of this paper is to investigate various inclusion relations and some other properties of a certain subclasses �p,k(�,A,B,n) and � ∗(�,A,B,n) of meromorphically p-valent analytic funtions with negative coefficients which are defined here by means of a linear operator. The familier concept of neighborhoods of analytic functions is also extended and applied to the functions considered here. We also derive many interesting results for the modified Hadamard products of functions belonging to the class � ∗(�,A,B,n).
NEIGHBOURHOODS OF UNIVALENT FUNCTIONS
Abstract The main result shows that a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighbourhood consisting entirely of univalent functions. For the particular choice of a linear function in the hypothesis of the main theorem, we obtain a corollary which is equivalent to the classical Noshiro–Warschawski–Wolff univalence criterion. We also present an application of the main result in terms of Taylor series, and we show that the hypothesis of our main result is sharp.
A certain family of meromorphically multivalent functions
Abstract By making use of a familiar analogue of the Ruscheweyh derivative as well as of the principle of subordination between two analytic functions, the authors introduce and study rather systematically a certain family of meromorphically multivalent functions in the open unit disk U≔{z:z∈ C and 0 Several inclusion properties of this family are associated with an integral operator of the Bernardi-Libera-Livingston type.