Coefficient Estimates for Some Subclasses of m-Fold Symmetric Bi-univalent Functions Defined by Linear Operator

Dhirgam Allawy Hussein   Hussein; Sahar Jaafar  Mahmood

doi:10.24297/jam.v20i.8976

Authors

Dhirgam Allawy Hussein Hussein Directorate of Education in Al-Qadisiyah , Diwaniyah , Iraq
Sahar Jaafar Mahmood Department of Multimedia, College of Computer Science and Information Technology, University of AlQadisiyah P.O. Box 88, Al Diwaniyah, Al-Qadisiyah, Iraq

DOI:

https://doi.org/10.24297/jam.v20i.8976

Keywords:

Analytic function, Univalent, Bi-univalent function, m-fold symmetric function, m-fold symmetric, bi-univalent function

Abstract

The articles introduces and investigates "two new subclasses of the bi-univalent functions ." These are analytical functions related to the m-fold symmetric function and . We calculate the initial coefficients for all the functions that belong to them, as well as the coefficients for the functions that belong to a field where finding these coefficients requires a complicated method. Between the remaining results, the upper bounds for "the initial coefficients "are found in our study as well as several examples. We also provide a general formula for the function and its inverse in the m-field. A function is called analytical if it does not take the same values twice . It is called a univalent function if it is analytical at all its points, and the function is called a bi-univalent if it and its inverse are univalent functions together. We also discuss other concepts and important terms. .

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