New subclass of analytic functions in conical domain associated with a linear operator

In this paper, we introduce and study a new subclass of analytic functions which are defined by means of a linear operator. Some results connected to coefficient estimates, growth and distortion theorems, radii of starlikeness, convexity close-to-convexity and integral means inequalities related to the subclass is obtained.

Gegenbauer polynomials constitute a numerical tool that has attracted the interest of many function theorists in recent times mainly due to their real-life applications in many areas of the sciences and engineering. Their applications in geometric function theory (GFT) have also been considered by many researchers. In this paper, this powerful tool is associated with the prolific concepts of convolution and subordination. The main purpose of the research contained in this paper is to introduce and study a new subclass of analytic functions. This subclass is presented using an operator defined as the convolution of the generalized distribution and the error function and applying the principle of subordination. Investigations into this subclass are considered in connection to Carathéodory functions, the modified sigmoid function and Bell numbers to obtain coefficient estimates for the contained functions.

A new differential operator Dα,λ,γ,βm is introduced and a new subclass of analytic functions with negative coefficients defined by this operator is investigated. Some results on coefficient inequalities, distortion theorems and extreme points of analytic functions belonging to the subclass are obtained.

By making use of an integral operator due to Noor, a new subclass of analytic functions, denoted by k–$\mathscr{UCV}_n$ (n $\in$ N0 := {0,1,2,...};0 ≤ k < ∞); is introduced. For this class the Fekete-Szego problem is completely settled. The results obtained here also give the Fekete-Szego inequalities for the classes of k-uniformly convex functions and k-parabolic starlike functions.

In the present paper, we have introduced a new subclass of analytic functions involving integral operator defined by polylogarithm function. Necessary and sufficient conditions are obtained for this class. Further distortion theorem, linear combination and results on partial sums are investigated.

This study introduces a novel linear operator incorporating both the Mittag-Leffler function and Lambert series to establish a new subclass of analytic functions denoted as . We first obtain sufficient conditions for functions to be members of . Consequently, we examine key properties including extreme points, coefficient constraints, and the radii of Univalency and starlikeness for functions in this subclass. In addition, by the means of Robin's inequalities, we provide some coefficients' lower bounds when applicable.

In this paper, we investigate certain subclass of analytic functions on the open unit disc. This class generalizes the well-known class of [Formula: see text]-convex functions with respect to n-symmetric points. Some interesting properties such as subordination results, containment relations, integral preserving properties, and the integral representation for functions in this class are obtained.

The objective of this paper is to introduce and investigate new subclass of analytic functions involving q−derivative Ruscheweyh operator. For functions belonging to this class, we obtain coefficient estimates on Taylor - Maclaurin series and the results on the famous Fekete Szego inequality.

The main objective of this paper is to introduce and study the generality differential operator involving the q-Mittag-Leffler function on certain subclasses of analytic functions. Also, we investigate the inclusion properties of these classes, by using the concept of subordination between analytic functions.

In this paper, we introduce new subclasses of analytic functions in the open unit disc. Furthermore, the necessary and sufficient conditions for the Poisson distribution series to be in these new subclasses are found.

This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order γ ( γ ∈ C \ 0 ) . This introduced a q-integral operator and certain subclasses of the newly introduced classes are defined by using this q-integral operator. Coefficient bounds for these subclasses are obtained. Furthermore, the ( δ , q )-neighborhood of analytic functions are introduced and the inclusion relations between the ( δ , q )-neighborhood and these subclasses of analytic functions are established. Moreover, the generalized hyper-Bessel function is defined, and application of main results are discussed.

In this paper, new subclasses of analytic functions in the open unit disk which are defined using generalized integral operator are introduced. Several interesting properties of these classes are obtained, such as inclusion relationships and integral preserving properties are derived.

A new subclass TXq[λ,A,B] of analytic functions is introduced by making use of the q-derivative operator associated with the Pascal distribution. Certain properties of analytic functions in the subclass TXq[λ,A,B] are derived. Some known results are generalized.

In this paper, a new subclass S∗(μ, β, ℘,Un(t)) of univalent functions is defined by using Opoola differential operator involving subordination principle. The upper bounds to the second Hankel determinant denoted by H2(2) for the subclass S∗(μ, β, ℘,Un(t)) is established in connection with Chebyshev polynomials of the second kind and Toeplitz determinants.

In this paper,we define a class of analytic functions $F_{\left( \beta ,\lambda \right) }\left( H,\alpha ,\delta ,\mu \right) ,$ satisfying the following subordinate condition associated with Chebyshev polynomials \begin{equation*} \left\{ \alpha \left[ \frac{zG^{^{\prime }}\left( z\right) }{G\left( z\right) }\right] ^{\delta }+\left( 1-\alpha \right) \left[ \frac{% zG^{^{\prime }}\left( z\right) }{G\left( z\right) }\right] ^{\mu }\left[ 1+% \frac{zG^{^{\prime \prime }}\left( z\right) }{G^{^{\prime }}\left( z\right) }% \right] ^{1-\mu }\right\} \prec H\left( z,t\right) , \end{equation*}% where $G\left( z\right) =\lambda \beta z^{2}f^{^{\prime \prime }}\left( z\right) +\left( \lambda -\beta \right) zf^{^{\prime }}\left( z\right) +\left( 1-\lambda +\beta \right) f\left( z\right) ,$ $0\leq \alpha \leq 1,$ $% 1\leq \delta \leq 2,$ $0\leq \mu \leq 1,$ $0\leq \beta \leq \lambda \leq 1$ and $t\in \left( \frac{1}{2},1\right] $. We obtain initial coefficients $% \left\vert a_{2}\right\vert $ and $\left\vert a_{3}\right\vert $ for this subclass by means of Chebyshev polynomials expansions of analytic functions in $\mathcal{D}.$ Furthermore, we solve Fekete-Szegö problem for functions in this subclass.We also provide relevant connections of our results with those considered in earlier investigations. The results presented in this paper improve the earlier investigations.