Estimating coefficients for certain subclasses of meromorphic and bi-univalent functions

Area of Science:

• Complex Analysis
• Geometric Function Theory

Background:

• Meromorphic functions are complex functions with isolated poles.
• Bi-univalent functions are functions where both the function and its inverse are univalent.

Purpose of the Study:

• Introduce two new subclasses of meromorphic and bi-univalent functions.
• Obtain coefficient bounds for functions within these subclasses.
• Explore related coefficient estimation problems.

Main Methods:

• Definition of novel subclasses of meromorphic and bi-univalent functions.
• Application of coefficient estimation techniques.
• Derivation of bounds for initial coefficients (e.g., a_1 and a_2).

Main Results:

• Established coefficient estimates for the newly defined function subclasses.
• Presented new coefficient bounds that are distinct from existing literature.
• Demonstrated the novelty of the derived coefficient inequalities.

Conclusions:

• The paper successfully introduced and characterized new subclasses of meromorphic and bi-univalent functions.
• The obtained coefficient bounds offer novel contributions to the field of geometric function theory.
• The methodology may be applicable to further research in related complex analysis problems.