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...

This article defines a new operator called the q-Babalola convolution by using quantum calculus and of normalized analytic functions in open unit disk. We then study class bi-univalent defined disk associated with operator. The main results investigation include some upper bounds for initial Taylor–Maclaurin coefficients Fekete–Szego inequalities class. Many applications finds are highlighted c...

The solutions provided in this work address the classic but still relevant topic of establishing new classes univalent functions linked to $q$-Chebyshev polynomials and examining coefficient estimates features. Aspects quantum calculus are also considered research make it more unique produce pleasing outcomes. We introduce connected polynomials, which generalize certain previously investigated ...

For λ ≥ 0 and 0 ≤ α < 1 < β, we denote by K (λ;α, β) the class of normalized analytic functions satisfying the two sided-inequality α << ( z f ′(z) f (z) + λ z2 f ′′(z) f (z) ) < β (z ∈ U), where U is the open unit disk. Let KΣ(λ;α, β) be the class of bi-univalent functions such that f and its inverse f −1 both belong to the class K (λ;α, β). In this paper, we establish bounds for the coefficie...

Subclasses of analytic and bi-univalent functions have been extensively improved utilized for estimating the Taylor–Maclaurin coefficients Fekete–Szegö functional. In this paper, we consider a certain subclass normalized functions. These inverses that possess continuation to an open unit disk are associated with orthogonal polynomials; namely, Gegenbauer polynomials satisfy subordination condit...

This paper presents a new general subfamily NΣmu,v(η,μ,γ,ℓ) of the family Σm that contains holomorphic normalized m-fold symmetric bi-univalent functions in open unit disk D associated with Ruscheweyh derivative operator. For belonging to introduced here, we find estimates Taylor–Maclaurin coefficients am+1 and a2m+1, consequences results are discussed. The current findings both extend enhance ...

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...

In this study, by using the concepts of subordination, we define a new family RM,N,λ,γ starlike functions complex order γ connected with cardioid domain. The main contribution article consists derivations sharp inequality, considering belonging to in U. Particularly, bounds first two Taylor–Maclaurin coefficients, estimates Fekete–Szegö-type functionals, and coefficient inequalities are investi...

The motivation of the present article is to define (p−q)-Wanas operator in geometric function theory by symmetric nature quantum calculus. We also initiate and explore certain new families holormorphic bi-univalent functions AE(λ,σ,δ,s,t,p,q;ϑ) SE(μ,γ,σ,δ,s,t,p,q;ϑ) which are defined unit disk U associated with operator. upper bounds for initial Taylor–Maclaurin coefficients Fekete–Szegö-type i...

In this paper, we define a new family of q-starlike and q-convex functions related to the cardioid domain utilizing ideas subordination Sălăgean quantum differential operator. The primary contribution article is derivation sharp inequality for newly established subclasses in open unit disc U. For novel family, bounds first two Taylor–Maclaurin coefficients, Fekete–Szegö-type functional, coeffic...