Serap Bulut

Bio: Serap Bulut is an academic researcher from Kocaeli University. The author has contributed to research in topics: Analytic function & Differential operator. The author has an hindex of 11, co-authored 68 publications receiving 475 citations. Previous affiliations of Serap Bulut include Balıkesir University.

Coefficient estimates for a general subclass of analytic and bi-univalent functions

Abstract: In this paper, we introduce and investigate an interesting subclass NΣh,p (λ, μ) of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class NΣh,p (λ, μ), we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|. The results presented in this paper would generalize and improve some recent works of Caǧlar et al. [3], Xu et al. [10], and other authors.

Chebyshev polynomial coefficient estimates for a class of analytic bi-univalent functions related to pseudo-starlike functions

Abstract: In this paper, we obtain initial coefficient bounds for functions belong to a subclass of analytic bi-univalent functions related to pseudo-starlike functions by using the Chebyshev polynomials and also we find Fekete-Szego inequalities for this class.

Faber Polynomial Coefficient Estimates for a Comprehensive Subclass of Analytic Bi-Univalent Functions Defined by Subordination

Abstract: In this paper, we find coefficient estimates by a new method making use of the Faber polynomial expansions for a comprehensive subclass of analytic bi-univalent functions, which is defined by subordinations in the open unit disk. The coefficient bounds presented in this paper would generalize and improve some recent works appeared in the literature.

Faber polynomial coefficient estimates for a subclass of analytic bi-univalent functions

Abstract: In this work, considering a general subclass of analytic bi-univalent functions, we determine estimates for the general Taylor-Maclaurin coefficients of the functions in this class. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coeffcient bounds.

Coefficient Bounds for a Certain Class of Analytic and Bi-Univalent Functions

Abstract: In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$ . By using the Faber polynomial expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic and bi-univalent function class. Some interesting recent developments involving other subclasses of analytic and bi-univalent functions are also briefly mentioned.

Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions

Abstract: Let $\Sigma$ denote the class of functions $$f(z)=z+\sum_{n=2}^{\infty}a_nz^n$$ belonging to the normalized analytic function class $\mathcal{A}$ in the open unit disk $\mathbb{U}$, which are bi-univalent in $\mathbb{U}$, that is, both the function $f$ and its inverse $f^{-1}$ are univalent in $\mathbb{U}$. The usual method for computation of the coefficients of the inverse function $f^{-1}(z)$ by means of the relation $f^{-1}\big(f(z)\big)=z$ is too difficult to apply in the case of $m$-fold symmetric analytic functions in $\mathbb{U}$. Here, in our present investigation, we aim at overcoming this difficulty by using a general formula to compute the coefficients of $f^{-1}(z)$ in conjunction with the residue calculus. As an application, we introduce two new subclasses of the bi-univalent function class $\Sigma$ in which both $f(z)$ and $f^{-1}(z)$ are $m$-fold symmetric analytic functions with their derivatives in the class $\mathcal{P}$ of analytic functions with positive real part in $\mathbb{U}$. For functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for $|a_{m+1}|$ and $|a_{2m+1}|$.