In this note we present a remark on the paper "On the coefficient inequalities for a class of holomorphic mappings associated with spirallike mappings in several complex variables" by Y.~Lai and Q.~Xu \cite{LX} published recently in the journal {\it Results in Mathematics}. We show that one of the theorems in \cite{LX} concerning the finite-dimensional space $\mathbb{C}^n$ is a direct consequence of another one, so it does not need an independent proof. Moreover, we prove that a sharp norm estimate on the Fekete--Szegö functional over spirallike mappings in a general Banach space can be deduced from a result in \cite{LX}.
We study the Fekete--Szegö problem on the open unit ball of a complex Banach space. Namely, the Fekete--Szegö inequalities are proved for the class of spirallike mappings relative to an arbitrary strongly accretive operator, and some of its subclasses. Next, we consider families of non-linear resolvents for holomorphically accretive mappings vanishing at the origin. We solve the Fekete--Szegö problem over these families.
In this paper, we obtain Fekete-Szegö inequality for the generalized bi-subordinate functions of complex order. The results, which are presented in this study, would generalize those in related works of several earlier authors.
In the present investigation, we derive Fekete-Szegö inequality for the class $\mathcal{S}^α_{\mathscr{L}_{g}}(ϕ)$, introduced here. In addition to that, certain applications of our results are also discussed.
In the present paper, a subclass of analytic and bi-univalent functions by means of (p; q)- Lucas polynomials is introduced. Certain coefficients bounds for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szego problem for this subclass is solved.
In the present paper, a new subclass of analytic and bi-univalent functions by means of Chebyshev polynomials is introduced. Certain coefficient bounds for functions belong to this subclass are obtained. Furthermore, the Fekete-Szego problem in this subclass is solved.
We extend our definition (in a recent paper \cite{KB}) of the coefficient determinants of analytic mappings of the unit disk to include many Fekete-Szeg$\ddot{o}$-type parameters, and compute the best possible bounds on certain specific determinants for the choice class of starlike functions.
The main purpose of this paper is to introduce a new comprehensive subclass of analytic close-to-convex functions and derive Fekete-Szegö inequalities for functions belonging to this new class by using a different way. Various known special cases of our results are also pointed out.
In this paper, two new subclasses of bi-univalent functions related to conic domains are defined by making use of symmetric $q$-differential operator. The initial bounds for Fekete-Szegö inequality for the functions $f$ in these classes are estimated.
In the present work, we propose to investigate the Fekete-Szegö inequalities certain classes of analytic and bi-univalent functions defined by subordination. The results in the bounds of the third coefficient which improve many known results concerning different classes of bi-univalent functions. Some interesting applications of the results presented here are also discussed.
In this paper we study an interpolation problem involving the Fekete--Szegö functional. It turns out that this problem links to the so-called filtration of infinitesimal generators. We introduce new filtration classes using the non-linear differential operator \[α\frac{f(z)}{z}+β\frac{zf'(z)}{f(z)}+(1-α-β)\left(1+\frac{zf''(z)}{f'(z)}\right)\] and establish certain properties of these classes. Sharp upper bounds of the modulus of the Fekete--Szegö functional over some filtration classes are found. We also present open problems for further study.
In this sequel to the recent work (see Azizi et al., 2015), we investigate a subclass of analytic and bi-univalent functions in the open unit disk. We obtain bounds for initial coefficients, the Fekete-Szegö inequality and the second Hankel determinant inequality for functions belonging to this subclass. We also discuss some new and known special cases, which can be deduced from our results.
In this paper we establish the coefficient bodies for a wide class of families of inverse functions. We also completely describe those functions that provide boundary points of that bodies in small dimensions. As an application we get sharp bounds for Fekete--Szegö functionals over some classes of functions defined by quasi-subordination as well as over classes of their inverses. As a biproduct we derive a formula for ordinary Bell polynomials that seems to be new.
We give coefficient estimates for a class of close-to-convex harmonic mappings, and discuss the Fekete-Szegő problem of it. We also introduce two classes of polyharmonic mappings $\mathcal{HS}_{p}$ and $\mathcal{HC}_{p}$, consider the starlikeness and convexity of them, and obtain coefficient estimates on them. Finally, we give a necessary condition for a mapping $F$ to be in the class $\mathcal{HC}_{p}$.
In this paper, we obtain the Fekete-Szegö problem for the $k$-th $(k\geq1)$ root transform of the analytic and normalized functions $f$ satisfying the condition \begin{equation*} 1+\frac{α-π}{2 \sin α}< {\rm Re}\left\{\frac{zf'(z)}{f(z)}\right\} < 1+\fracα{2\sin α} \quad (|z|<1), \end{equation*} where $π/2\leq α<π$. Afterwards, by the above two-sided inequality we introduce and investigate a certain subclass of analytic and bi-univalent functions in the disk $|z|<1$ and obtain upper bounds for the first few coefficients and Fekete-Szegö problem for functions belonging to this analytic and bi-u…
