On Neighborhoods of a New Class of Meromorphic Multivalent Functions with Negative Coefficients
DOI:
https://doi.org/10.58987/27zjre82Keywords:
Coefficient estimates, Generalized derivative operator, Meromorphic multivalent functions, Neighborhood propertiesAbstract
In this paper, we introduce an extension of the generalized derivative operator Iᵐv(λ1, λ2, l, n) f(z), from the field of multivalent analytic functions in the open unit disc to the field of meromorphic multivalent functions in the punctured open unit disc. Then we introduce and systematically study a new class Ҡᵐv(λ1, λ2, l, n, ϖ, ꙋ) of meromorphic multivalent functions in the punctured open unit disc by means of a new extended generalized derivative operator Iᵐv(λ1, λ2, l, n) f(z). This class of functions is defined by a condition involving the proposed extended operator, which gave this class new geometric and analytical properties. Membership in this class is characterized by coefficient estimates. In addition, the inclusion and neighborhood properties of this class of functions are investigated.
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