Certain subclasses of bi-univalent functions connected with polylogarithm function

In this study, we present two novel subclasses of bi-univalent functions defined in the open unit disk, utilizing Liouville–Caputo fractional derivatives. We find constraints on initial Taylor coefficients |c2|, |c3| for functions in these subclasses of bi-univalent functions. Additionally, by using the values of a2,a3 we determine the Fekete–Szegö inequality results. Moreover, a few new subclasses are deduced that have not been studied in relation to Liouville–Caputo fractional derivatives so far. The implications of the results are also emphasized. Our results are concrete examples of several earlier discoveries that are not only improved but also expanded upon.

In this paper we discuss some newly constructed subclasses of bi-univalent functions and establish bounds for the coefficients of the functions in the subclasses SΣ(λ, α) and SΣ(λ, β).

The aim of this paper is to study certain subclasses of bi-univalent functions defined by generalized Sãlãgean differential operator related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients a2 and a3 and upper bounds for the Fekete-Szegö functional for the functions in this class. The results proved by various authors follow as particular cases.

In this paper, we introduce three new subclasses of the function class $\Sigma^{\prime}$ of bi-univalent functions involving the Poisson distribution associated with Horadam polynomials. Furthermore, we obtain estimates on the first two coefficients of functions in these new subclasses. Also, Fekete-Szegö inequalities of functions belonging to these subclasses are founded.

In this present paper, the author construct a new class $S_{\lambda, \delta}^{k, \alpha}(\gamma, t, \Psi)$ of bi-univalent functions of complex order defined in the open unit disc. The second and the third coefficients of the Taylor-Maclaurin series for functions in the new subclass are determined. Several special consequences of the results are also pointed out.

The main purpose of this paper is to obtain an upper bound for the second Hankel determinant for functions belonging to a subclass of bi-univalent functions in the open unit disk in the complex plane. Furthermore, the presented results in this work improve or generalize the recent works of other authors.

In the present paper, we have introduced a new subclass of analytic functions involving integral operator defined by polylogarithm function. Necessary and sufficient conditions are obtained for this class. Further distortion theorem, linear combination and results on partial sums are investigated.

A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems

Let Ω denote the class of functions f ( z ) = z + a 2 z 2 + a 3 z 3 + ⋯ belonging to the normalized analytic function class A in the open unit disk U = z : z < 1 , which are bi-univalent in U , that is, both the function f and its inverse f − 1 are univalent in U . In this paper, we introduce and investigate two new subclasses of the function class Ω of bi-univalent functions defined in the open unit disc U , which are associated with a new differential operator of analytic functions involving binomial series. Furthermore, we find estimates on the Taylor–Maclaurin coefficients | a 2 | and | a 3 | for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

In the contemporary paper, we introduce new subclasses of analytic and bi-univalent functions involving integral operator based upon Lucas polynomial. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients a2 and a3 for functions in these subclasses and obtain Fekete-Szegö problem for these subclasses.

‎In this paper‎, ‎we introduce and investigate a subclass‎ of analytic and bi-univalent functions which both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric in the open unit disk U‎. Furthermore‎, ‎we find upper bounds for the initial coefficients $|a_{m‎ + ‎1}|$ and $|a_{2m‎ + ‎1}|$ for functions in this subclass‎. ‎The results presented in this paper would generalize and improve some recent works‎.

The q-derivative and Hohlov operators have seen much use in recent years. First, numerous well-known principles of the q-derivative operator are highlighted and explained in this research. We then build a novel subclass of analytic and bi-univalent functions using the Hohlov operator and certain q-Chebyshev polynomials. A number of coefficient bounds, as well as the Fekete–Szegö inequalities and the second Hankel determinant are provided for these newly specified function classes.

In this article, we introduce a new subclass of analytic bi-univalent functions using the Ruscheweyh type q-analogue operator. In addition, we estimate upper bounds for general and early bounds of Taylor-Maclaurin coefficients in functions of the class which is considered by using Faber polynomial expansions.

This paper presents two subclasses of analytic and bi-univalent functions associated with the Ruscheweyh derivative operator to investigate the bounds for and where and are the initial Tayler-Maclaurin coefficients. The current results would generalize and improve some corresponding recent works. Additionally, in certain cases, our estimates correct some of the existing coefficient bounds.

In this paper, estimates for second and third MacLaurin coefficients of a new subclass of analytic and bi-univalent functions in the open unit disk are determined, and certain special cases are also indicated