In this paper, we define new subclasses ${S}^{*}_{q}(alpha,Phi),$ ${M}_{q}(alpha,Phi)$ and ${L}_{q}(alpha,Phi)$ of analytic functions in the space of logistic sigmoid functions based on quasi--subordination and determine the initial coefficient estimates $|a_2|$ and $|a_3|$ and also determine the relevant connection to the classical Fekete--Szeg"o inequalities. Further, we discuss the improved ...

In the present investigation, we use the Horadam Polynomials to establish upper bounds for the second and third coefficients of functions belongs to a new subclass of analytic and $lambda$-pseudo-starlike bi-univalent functions defined in the open unit disk $U$. Also, we discuss Fekete-Szeg$ddot{o}$ problem for functions belongs to this subclass.

‎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 this paper, two new subclasses of holomorphic and bi-univalent functions are introduced by using Balancing polynomials. Then, coefficient estmations determined for the first coefficients belonging to these classses. Finally, Fekete-Szeg¨o problem is handled in defined.

In the present investigation, inspired by work on Yamaguchi type class of analytic functions satisfyingthe criteria $\mathfrak{Re}\{\frac{f (z)}{z}\} > 0, $ in openunit disk $\Delta=\{z \in \mathbb{C}\colon |z|<1\}$ and making use S\v{a}l\v{a}gean-difference operator, which is a special Dunkl operator with constant $\vartheta$ $\Delta$ , wedesignate definite new classes $\mathcal{R}_{\lam...

By making use of $q$-derivative and $q$-integral operators, we define a class analytic bi-univalent functions in the unit disk $|z|<1$. Subsequently, investigate some properties such as early coefficient estimates then obtain Fekete-Szeg\"o inequality for both real complex parameters. Further, interesting corollaries are discussed.