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).
Majorization Problem for Certain Classes of Meromorphic Multivalent Functions Defined by Differential Operator
In this paper, we investigate the majorization problem of certain classes of meromorphic multivalent functions defined by differential operator.
On certain classes of meromorphically p-valent starlike functions
Abstract Let Mn+p−1 (α) denote the class of functions of the form f(z) = 1 zp + a 0 zp−1 + ⋯ + a k+p−1 z k +⋯, p ∈ N = {1, 2, 3,…}, that are regular in the annulus D = {z : 0 re z(D n+p− 1 ƒ(z))′ D n+p− 1 ƒ(z) for 0 ≤ α D n+p− 1 ƒ(z) = 1 z p z n+p− 1 ƒ(z) (n + p − 1 )! (n+p− 1 ) We prove that Mn+p(α) ⊂ Mn+p-1(α), where n is any integer greater than −p. We also consider some integrals of functions in the class Mn+p−1(α).