Inequalities on coefficients for certain classes of m-fold symmetric and bi-univalent functions equipped with Faber polynomial

Abstract

In this work, considering a new subclass of bi-univalent functions which are m-fold symmetric and analytic functions in the open unit disk, we determine estimates for the general Taylor-Maclaurin coefficient of the functions in this class. Furthermore, initial upper bounds of coefficients for m-fold symmetric, analytic and bi-univalent functions were found in this study. For this purpose, we used the Faber polynomial expansions. In certain cases, the coefficient bounds presented in this paper would generalize and improve some recent works in the literature. We hope that this paper will inspire future researchers in applying our approach to other related problems.

Coefficient Bounds for a New Families of m-Fold Symmetric Bi-Univalent Functions Defined by Bazilevic Convex Functions

“…We denote by D the family of -fold symmetric bi-univalent functions in . It is easily seen that for = 1, the formula (1.4) coincides with the formula (1.2) of the family D. Some examples of -fold symmetric bi-univalent functions are given as follows: Recently, many authors investigated bounds for various subfamilies of -fold biunivalent functions (see [4,7,13,18,20,21,24,26,27,31,32]).…”

Certain Class of Bi-Univalent Functions Defined by Sălăgean q-Difference Operator Related with Involution Numbers

“…The study of bi-univalent functions gained momentum mainly due to the work of Srivastava et al [17]. Motivated by this, many researchers [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] (also the references cited therein) recently investigated several interesting subclasses of the class Σ and found non-sharp estimates on the first two Taylor-Maclaurin coefficients. Motivated by recent study on telephone numbers [34] and using the Sȃlȃgean q-differential operator defined by ( 5), for functions ξ of the form (7) as given in [33], we have…”

Solving Bisymmetric Solution of a Class of Matrix Equations Based on Linear Saturated System Model Neural Network

“…In order to reduce the training time of the model, the deep learning network is combined with the hierarchical training mechanism, and the maximum likelihood function learning method is used to train each layer of data [15]. e LSSM neural network structure is used to train the eigenvalues of matrix bisymmetric solution [16]. e multiple term transformation is used to extract the eigenvalues step by step.…”