In this paper, we introduce a special family Mσm(τ,ν,η,φ) of the function σm m-fold symmetric bi-univalent functions defined in open unit disc D and obtain estimates first two Taylor–Maclaurin coefficients for family. Further, Fekete–Szegö functional is also estimated. The results presented paper not only generalize improve some recent works, but give new as cases.

The paper introduces a new family of analytic bi-univalent functions that are injective and possess inverses, by employing q-analogue the derivative operator. Moreover, article establishes upper bounds Taylor–Maclaurin coefficients these functions, which can aid in approximating accuracy approximations using finite number terms. obtained Faber polynomial expansions. These apply to both initial ...

We introduce and examine two new subclass of bi-univalent function Σ, defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to involution numbers. find initial estimates Taylor–Maclaurin coefficients |a2| |a3| for functions introduced here. also obtain a Fekete–Szegö inequality class. Several consequences our results pointed out, not yet discussed as...

In this article we introduce three new subclasses of the class bi-univalent functions Σ, namely HGΣ, GMΣ(μ) and GΣ(λ), by using subordinations with whose coefficients are Gregory numbers. First, evidence that these classes not empty, i.e., they contain other besides identity one. For in each function classes, investigate estimates a2 a3 Taylor–Maclaurin Fekete–Szegő functional problems. The mai...

The zero-truncated Poisson distribution is an important and appropriate model for many real-world applications. Here, we exploit the probabilities to construct a new subclass of analytic bi-univalent functions involving Gegenbauer polynomials. For in constructed class, explore estimates Taylor–Maclaurin coefficients a2 a3, next, solve Fekete–Szegő functional problem. A number interesting result...