In this paper, we define certain families SE*(?) and CE(?) of holomorphic bi-univalent functions which are defined in the open unit disk U. We establish upper bounds for initial Taylor–Maclaurin coefficients Fekete–Szegö type inequalities these families.

Suppose that f : C → C and g : C → C is defined by g(x) = f(t · x) where t ∈ C is fixed and t · x = t1x1 + · · · + tdxd. In the case of t = iω with ω ∈ R and f(z) = e, g(x) = e and hence we refer to t as a (generalized) “frequency”. Such an g is called a ridge function (or sometimes a planar wave). If we have n such frequencies t1, . . . , tn ∈ C then the span of the associated ridge functions ...

In this study, we introduce and examine a certain subclass of analytic functions in the open unit disk complex plane. Here, give coefficient bound estimates investigate Fekete-Szegö problem for introduced class. Some interesting special cases results obtained here are also discussed.

In this paper, we introduce two new subclasses of bi-univalent functions using the q-Hermite polynomials. Furthermore, establish bounds initial coefficients υ2, υ3, and υ4 Taylor–Maclaurin series that Fekete–Szegö functional associated with classes, give many consequences our findings.

In geometric function theory, Lucas polynomials and other special have recently gained importance. this study, we develop a new family of bi-univalent functions. Also examined coefficient inequalities Fekete-Szegö problem for via these polynomials.

Bartha D. (szerk.) (2019): Vörös Lista – Magyarország fa- és cserjefajai. Soproni Egyetemi Kiadó, Sopron, 59 pp. ISBN 978-963-334-328-9
 (2020): Fekete Lista. inváziós ● Szürke potenciálisan 84 978-963-334-357-9

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.