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).
A Certain Subclass of Meromorphically Multivalent Analytic Functions with Negative Coefficients
The paper aims to introduce a certain subclass S*g(A,B,I±,p,j) of the class I£*(p) of meromorphically multivalent functions with negative coefficients, defined by using the definitions of Hadamard product and subordination for two functions belong to the class I£*(p). We first investigate the geometric characterization property, giving the coefficient estimates for functions in the class S*g(A,B,I±,p,j). We also obtain the distortion theorem, radii of meromorphically p-valent starlikeness and convexity of order (0â¤I³
Some convolution conditions for starlikeness and convexity of meromorphically multivalent functions
By making use of the Hadamard product (or convolution), the authors derive necessary and sufficient conditions for a suitably normalized meromorphically p-valent function to be in the familiar classes of meromorphic p-valently starlike and meromorphic p-valently convex functions in the punctured unit disk.