On Subclass of Meromorphic Analytic Functions Defined by a Differential Operator

Abstract

Abstract In this work, using the differential operator and the concept of meromorephic analytic functions we introduce and investigate the class Σ β , λ α , m ( A , B , Y , β ) , of functions of the form f ( z ) = z − 1 + ∑ n = 1 ∞ a n z n , a n ≥ 0 , which are analytic and meromorphic univalent in the punctured unit disk U * = { z ∈ C : 0 < | z | < 1 } , satisfying | A [ γ z 2 ( D β , λ α , m f ( z ) ) ′ ′ ′ + z ( 3 Υ + β ) ( D β , λ α , m f ( z ) ) ′ ′ + ( Υ + β ) ( D β , λ α , m f ( z ) ) ′ ] B [ Υ z ( D β , λ α , m f ( z ) ) ′ ′ + ( Υ + β ) ( D β , λ α , m f ( z ) ) ′ ] | < 1 . Further, coefficient bounds, Hadamard product, radius of close to-convexity, inclusive properties and neighbourhoods of functions in our class are obtain.