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

In this paper, we establish the coefficient bodies for a wide class of families inverse functions. We also completely describe functions that are boundary points these in small dimensions. use to obtain sharp bounds Fekete–Szegö functionals over some classes defined by quasi-subordination as well their inverses. As biproduct, derive formula ordinary Bell polynomials seems be new.

‎Universally prestarlike functions of order $alphaleq 1$ in the‎ ‎slit domain $Lambda=mathbb{C}setminus [1,infty)$ have been‎ ‎recently introduced by S‎. ‎Ruscheweyh.This notion generalizes the‎ ‎corresponding one for functions in the unit disk $Delta$ (and‎ ‎other circular domains in $mathbb{C}$)‎. ‎In this paper‎, ‎we obtain‎ ‎the Fekete-Szegö coefficient functional for transforms of such‎ ‎f...

In the present paper, a subclass of analytic and biunivalent functions by means Gegenbauer polynomials is introduced. Certain coefficients bound for belonging to this are obtained. Furthermore, Fekete-Szegö problem solved. A number known or new results shown follow upon specializing parameters involved in our main results.

In this note we present a remark on the paper “On coefficient inequalities for class of holomorphic mappings associated with spirallike in several complex variables” by Y. Lai and Q. Xu [10] published recently journal Results Mathematics. We show that one theorems concerning finite-dimensional space $${{\mathbb {C}}}^n$$ is direct consequence another one, so it does not need an independent proo...