The purpose of this article is to derive the necessary and sufficient conditions for the power series 〖P℘〗_(ℷ,γ)^μ (t) whose coefficients are probabilities of the beta negative binomial distribution to be in the family F(σ,τ,ϵ,η,μ,ℷ,γ) of holomorphic functions which are defined in the open unit disk. We establish a number of important geometric properties, such as, coefficient estimates, extreme points, neighborhood property, integral representation, radii of starlikeness and convexity and Hadamard product properties for functions belongs to this family. Also we determinate some differential subordination properties of the power series 〖P℘〗_(ℷ,γ)^μ (t).
In the current work, we use the (M,N)-Lucas Polynomials to introduce a new families of holomorphic and bi-Prestarlike functions defined in the unit disk O and establish upper bounds for the second and third coefficients of the Taylor-Maclaurin series expansions of functions belonging to these families. Also, we debate Fekete-Szeg¨o problem for thesefamilies. Further, we point out several certain special cases for our results.
In this work, we submite and study a newlclass of meromorphiccmultivalent functions defined by fractional differ-integral operator . We gain some geometric properties , such as, coefficient inequality, growth and distortion bounds, convolution properties, integral representation, radii of starlikeness and convexity, extreme points, weighted mean and arithmetic mean for functions belonging to the class
The purpose of the present paper is to introduce and investigate two new general subclasses $\mathcal{M} \mathcal{A}_{\Sigma_{m}}(\delta, \lambda ; \alpha)$ and $\mathcal{M} \mathcal{A}_{\Sigma_{m}}(\delta, \lambda ; \beta)$ of $\Sigma_{m}$ consisting of holomorphic and m-fold symmetric bi-univalent functions defined in the open unit disk $U$. For functions belonging to the two classes introduced here, we derive estimates on the initial coefficients $\left|d_{m+1}\right|$ and $\left|d_{2 m+1}\right|$. We get new special cases for our results. In addition, Several related classes are also investigated and connections to earlier known outcomes are made.
In this paper, we define a new class of harmonic univalent functions of the form in the open unit disk . We obtain basic properties, like, coefficient bounds, extreme points, convex combination, distortion and growth theorems and integral operator.
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