Estimates of Coefficients for Bi-Univalent Functions in the Subclass H_∑ (n,γ,φ) - Khalid I. Abdullah; Nafya H. Mohammed (Tikrit Journal of Pure Science, 2023)
Considering that finding the bounds for the coefficients of the Taylor-Maclaurin series expansion of bi-univalent functions is one of the important subjects in geometric function theory that has attracted the attention of many researchers in the last few decades, we also take a step in this direction. Finding such bounds is the main focus or, more clearly, the main problem of our work. In this article, we study the subclass H_∑ (n,γ,φ) of bi-univalent functions which is defined in the open unit disk D. Furthermore, we obtained the upper bounds estimates for the first coefficients |a_2 | and |a_3 | of the functions in this category by using subordination method. From the main result of the article (Theorem 2.1), special cases have been derived that improve some the results of previous articles.