Some estimation about Tayler-Maclaurin coefficients of generalized subclasses of bi-univalent functions

A Comprehensive Subclass of Bi-Univalent Functions Associated with Chebyshev Polynomials of the Second Kind

Our objective in this paper is to introduce and investigate a newly-constructed subclass of normalized analytic and bi-univalent functions by means of the Chebyshev polynomials of the second kind. Upper bounds for the second and third Taylor-Maclaurin coefficients, and also Fekete-Szego inequalities of functions belonging to this subclass are founded. Several connections to some of the earlier known results are also pointed out.

Sub classes of Bi-Univalent Functions Defined by Salagean type $q-$ Difference Operator

In this paper, we introduce and investigate a new subclass of the function class $Σ$ of bi-univalent functions defined in the open unit disk, which are associated with the Sălăgean type $q-$ difference operator and satisfy some subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for functions in the new subclass introduced here. Several (known or new) consequences of the results are also pointed out. Further we obtain Fekete-Szeg$\ddot{o}$ inequality for the new function class.

Faber polynomial coefficient estimation of subclass of bi-subordinate univalent functions

In this paper, a comprehensive subclass of bi-univalent functions class are introduced and investigated. Using the Faber polynomials, estimation of the coefficients $|a_n|$ and certain Fekete-Szegö inequality of Maclaurin expansion of functions in this subclass are concluded. Finally, some earlier results are pointed out and improved.

New Subclasses of Analytic and Bi-Univalent Functions Endowed with Coefficient Estimate Problems

Inspired by the recent works of Srivastava et al. (2010), Frasin and Aouf (2011), and Caglar et al. (2013), we introduce and investigate in the present paper two new general subclasses of the class consisting of normalized analytic and bi-univalent functions in the open unit disk U. For functions belonging to these general subclasses introduced here, we obtain estimates on the Taylor-Maclaurin coefficients |a_2| and |a_3|. Several connections to some of the earlier known results are also pointed out. The results presented in this paper would generalize and improve those in related works of sev…

Certain classes of bi-univalent functions related to Shell-like curves connected with Fibonacci numbers

Recently, in their pioneering work on the subject of bi-univalent functions, Srivastava et al. \cite{HMS-AKM-PG} actually revived the study of the coefficient problems involving bi-univalent functions. Inspired by the pioneering work of Srivastava et al. \cite{HMS-AKM-PG}, there has been triggering interest to study the coefficient problems for the different subclasses of bi-univalent functions. Motivated largely by Ali et al. \cite{Ali-Ravi-Ma-Mina-class}, Srivastava et al. \cite{HMS-AKM-PG} and Güney et al. \cite{HOG-GMS-JS-Fib-2018} in this paper, we consider certain classes of bi-univalent…

Coefficient Estimates for Certain Subclass of Bi Functions Associated the Horadam Polynomials

In the present article, our goal is finding estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for a new class of bi-univalent functions defined by means of the Horadam polynomials. Fekete-Szego inequalities of functions belonging to this subclass are also founded.

Coefficient estimates for some families of bi-bazilevic functions of the ma-minda defined by convolution

Making use of the Hadamard product(or convolution), we find some estimates on the Taylor-Maclaurin coefficients $|a_{2}|$ and $|a_{3}|$ for functions belong to bi univalent functions of the Bazilevi$\check{c}$ type of order $γ$. Several (known or new) consequences of the results are also pointed out.

广义三角函数的解析延拓

Analytic Continuation of Generalized Trigonometric Functions

通过统一的几何方法，将具有两个参数的广义三角函数解析延拓到其单叶的最大定义域，并推导了麦克劳林级数收敛半径、与旋转的交换性、单叶域外的延拓以及周期性等结论。

Coefficient estimate of bi-Bazileviuc function of complex order based on quasi subordination involving Srivastava-Attiya operator

In this paper, we introduce and investigate a new subclass of the function class $Σ$ of bi-univalent functions defined in the open unit disk, which are associated with the Hurwitz-Lerch zeta function, satisfying quasi-subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for functions in this new subclass. Several (known or new) consequences of the results are also pointed out.