Author:
Wanas Abbas Kareem,Al-Ziadi Najah Ali Jiben
Abstract
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).
Reference35 articles.
1. R. M. Ali, V. Ravichandran and N. Seenivasagan, Differential subordination and superordination of analytic functions defined by the Dziok-Srivastava operator, J. Franklin Inst. 347 (2010), 1762-1781. https://doi.org/10.1016/j.jfranklin.2010.08.009
2. S. Altinkaya and S. Yalçin, Poisson distribution series for certain subclasses of starlike functions with negative coefficients, An. Univ. Oradea Fasc. Mat. 24(2) (2017), 5-8.
3. A. A. Amer and M. Darus, Some properties of the class of univalent functions with negative coefficients, Applied Mathematics 3 (2012), 1851-1856. https://doi.org/10.4236/am.2012.312251
4. A. Amourah and M. Darus, Some properties of a new class of univalent functions involving a new generalized differential operator with negative coefficients, Indian J. Sci. Tech. 9(36) (2016), 1-7. https://doi.org/10.17485/ijst/2016/v9i36/97738
5. M. K. Aouf, A. O. Mostafa and O.M. Algubouri, Some families of uniformly starlike and convex functions with negative coefficients, Acta Univ. Apulensis 45 (2016), 125-147.
Cited by
14 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献