Coefficient Estimates for New Subclasses of Meromorphic Bi-Univalent Functions

Area of Science:

• Complex Analysis
• Geometric Function Theory

Background:

• Bi-univalent functions are a subclass of analytic functions with the property that both the function and its inverse are analytic.
• Meromorphic functions are functions that are analytic except for simple poles.
• The study of coefficient estimates is crucial for understanding the geometric properties of function classes.

Purpose of the Study:

• To introduce and define two new subclasses of meromorphic bi-univalent functions.
• To investigate the properties of these newly defined function classes.
• To obtain coefficient estimates for functions belonging to these subclasses.

Main Methods:

• Definition of new subclasses of meromorphic bi-univalent functions.
• Application of analytical techniques to derive coefficient bounds.
• Utilizing properties of functions defined on the domain Δ = {z : z ∈ ℂ, 1 < |z | <∞}.

Main Results:

• Introduction of the subclasses ℳ σ (α, λ) and ℳ σ (β, λ).
• Derivation of estimates for the initial coefficients (e.g., |f(0)|, |f'(0)|) of functions in these classes.
• Establishment of bounds that characterize the behavior of these functions.

Conclusions:

• The study successfully introduced and characterized new subclasses of meromorphic bi-univalent functions.
• The obtained coefficient estimates provide valuable information about the geometric properties of these functions.
• This research contributes to the ongoing exploration of bi-univalent functions in complex analysis.