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...

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 ...

In this paper, we define two classes of meromorphic multivalent functions in the punctured disc U*=w∈C:0<|w|<1 by using principle subordination. We investigate a number useful results including subordination results, some connections with certain integral operator, sandwich properties, an inclusion relationship, and Fekete-Szegö inequalities for belonging these classes. Our are connected ...

One of the most important problems in study geometric function theory is knowing how to obtain sharp bounds coefficients that appear Taylor–Maclaurin series univalent functions. In present investigation, our aim calculate some estimates involving for family convex functions with respect symmetric points and associated a hyperbolic tangent function. These include first four initial coefficients,...

In this research, a novel linear operator involving the Borel distribution and Mittag-Leffler functions is introduced using Hadamard products or convolutions. This utilized to develop new subfamilies of bi-univalent via principle subordination with Gegenbauer orthogonal polynomials. The investigation also focuses on estimation coefficients |a?|(?=2,3) Fekete–Szegö inequality for belonging these...

In this paper, we define a subclass of analytic functions by denote $T_{\beta}H\left( z,C_{n}^{\left( \lambda \right) }\left( t\right) $ satisfying the following subordinate condition \begin{equation*} \left( 1-\beta \frac{zf^{^{\prime }}\left( z\right) }{f\left( }\right) +\beta 1+\frac{zf^{^{\prime \prime }{f^{^{\prime \prec \frac{1}{\left( 1-2tz+z^{2}\right) ^{\lambda }}, \end{equation*} wher...

In this paper, we consider a class L (λ, μ;φ) of analytic functions f defined in the open unit disk U satisfying the subordination condition that q(z) Df(z) Dλf(z) ≺ φ(z) (λ ∈ N0, μ ≥ 0; z ∈ U), where q(z) = ( z Dλf(z) )μ−2 , D is the Sălăgean operator and φ(z) is a convex function with positive real part in U. We obtain some characteristic properties giving the coefficient inequality, radius a...