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

## 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

## 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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D.A. Hussein, A.K. Wanas and S.J. Mahmood, coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions ,Journal of SJU,55,(3)(2020).

2021-03-25

## How to Cite

Hussein , D. A. H. ., & Mahmood , S. J. . (2021). Coefficient Estimates for Some Subclasses of m-Fold Symmetric Bi-univalent Functions Defined by Linear Operator. JOURNAL OF ADVANCES IN MATHEMATICS, 20, 115–120. https://doi.org/10.24297/jam.v20i.8976

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