A parabolic starlike function f of order ρ in the unit disk is characterized by the fact that the quantity z f ′(z)/ f (z) lies in a given parabolic region in the right half-plane. Denote the class of such functions by PS∗(ρ). This class is contained in the larger class of starlike functions of order ρ. Subordination results for PS∗(ρ) are established, which yield sharp growth, covering, and di...

In the present paper, a general subclass Mh,p ?m (?, ?) of m-Fold symmetric bi-univalent functions is de?ned. Also, estimates TaylorMaclaurin coefficients |am+1|, |a2m+1| and Fekete-Szegö problems are obtained for in this new subclass. The results presented paper would generalize improve some recent works several earlier authors.

In this paper, by using the concept of symmetric q -difference operator, we introduce certain classes id="M4"> -starlike and id="M5"> -convex functions. Convolution results, coefficient estimates, Fekete–Szegö inequalities for analytic functions belonging to these are obtained.

Let H be the class of functions f(z) of the form f(z) = z + ∑∞ n=2 anz , which are analytic in the unit disk U = {z : |z| < 1}. In this paper, the authors introduce a subclass M (α, λ, ρ) of H and study its some properties. The subordination relationships, inclusion relationships, coefficient estimates, the integral operator and covering theorem are proven here for each of the function classes....

Motivated by the study of spectral properties of self-adjoint operators in the integral group ring of a sofic group, we define and study integer operators. We establish a relation with classical potential theory and in particular the circle of results obtained by M. Fekete and G. Szegö, see [Fek23,FS55,Sze24]. More concretely, we use results by R. Rumely, see [Rum99], on equidistribution of alg...

The aim of this paper is to introduce some special families holomorphic and S\u{a}l\u{a}gean type bi-univalent functions by making use Horadam polynomials involving the modified sigmoid activation function $\phi(s)=\frac{2}{1+e^{-s} },\,s\geq0$ in open unit disc $\mathfrak{D}$. We investigate upper bounds on initial coefficients for form $g_{\phi}(z)=z+\sum\limits_{j=2}^{\infty}\phi(s)d_jz^j$, ...

Motivated by q-calculus, we define a new family of Σ, which is the bi-univalent analytic functions in open unit disc U that related to Einstein function E(z). We establish estimates for first two Taylor–Maclaurin coefficients |a2|, |a3|, and Fekete–Szegö inequality a3−μa22 belong these families.

In the present article, using subordination principle, authors employed certain generalized multiplier transform to define two new subclasses of analytic functions with respect symmetric and conjugate points. particular, bi-univalent conditions for function f(z) belonging these their relevant connections famous Fekete-Szegö inequality |a3−va22| were investigated a succinct mathematical approach.

In this study, a new class RΣμ(x,γ,α,δ,β) of bi-univalent functions studied by means Gegenbauer polynomials (GP) with Rabotnov is introduced. The coefficient the Taylor coefficients a2 and a3 Fekete-Szegö problems for belonging to have been derived as well. Furthermore, variety results will appear considering parameters in main results.