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Estimates on Initial Coefficients of Certain Subclasses of Bi-Univalent Functions Associated with Al-Oboudi Differential Operator


Affiliations
  • All India Shri Shivaji Memorial Society's College of Engineering, Department of First Year Engineering, Pune, India
  • Willingdon College, Department of Mathematics, Sangli, India
     

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In the present investigation we introduce two subclasses ΝΣδ,μ [η, α, λ] and ΝΣδ,μ (η, β, λ) of the function class Σ of bi-univalent functions defined in the open unit disk. These subclasses are defined by using the Al-Oboudi differential operator, which is the generalized Salagean's differential operator. Also we find estimates on initial coeffcients |a2| and |a3| for the functions in these subclasses and consider some related subclasses in connection with these subclasses.

Keywords

Univalent Functions, Bi-Univalent Functions, Al-Oboudi Differential Operator, Salagean's Differential Operator.
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  • Estimates on Initial Coefficients of Certain Subclasses of Bi-Univalent Functions Associated with Al-Oboudi Differential Operator

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Authors

Amol B. Patil
, India
Uday H. Naik
, India

Abstract


In the present investigation we introduce two subclasses ΝΣδ,μ [η, α, λ] and ΝΣδ,μ (η, β, λ) of the function class Σ of bi-univalent functions defined in the open unit disk. These subclasses are defined by using the Al-Oboudi differential operator, which is the generalized Salagean's differential operator. Also we find estimates on initial coeffcients |a2| and |a3| for the functions in these subclasses and consider some related subclasses in connection with these subclasses.

Keywords


Univalent Functions, Bi-Univalent Functions, Al-Oboudi Differential Operator, Salagean's Differential Operator.

References