Analitik fonksiyonlar teorisinde Pascal tipi dağılım serileri ile uygulamaları üzerine bir çalışma

Bu güncel çalışmada, formundaki Pascal tipli dağılım serisi kullanılarak iki kuvvet serisi ve tanımlanmıştır. Daha sonra bu serilerin USTN(β) analitik fonksiyon sınıfına ait olması için gerekli şartlar geliştirilmiştir.

Anahtar Kelimeler:

Analitik fonksiyonlar, Dağılım serileri, Yıldızıl fonksiyonlar

A study on the Pascal type distribution series with applications in analytic function theory

In this current study, by using the Pascal type distribution series of the form we define two power series and Afterwards, we develop sufficient conditions for these series to be in the class USTN(β) of analytic functions.

Keywords:

Analytic functions, Distribution series, Starlike functions,

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Altınkaya, Ş. and Yalçın, S. (2017). Poisson distribution series for certain subclasses of starlike functions with negative coefficients. Annals of Oradea Universty Mathematics Fascicola, 24(2), 5-8.
Bulboaca, T. and Murugusundaramoorthy, G. (2020). Univalent functions with positive coefficients involving Pascal distribution series. Communications of the Korean Mathematical Society, 35(3), 867-877. https://doi.org/10.4134/CKMS.c190413
El-Deeb, S., Bulboaca, T. and Dziok, J. (2019). Pascal distribution series connected with certain subclasses of univalent functions. Kyungpook Mathematical Journal, 59(2), 301-314. https://doi.org/10.5666/KMJ.2019.59.2.301
Frasin, B. (2020). Subclasses of analytic functions associated with Pascal distribution series. Advances in the Theory of Nonlinear Analysis and its Applications, 4(2), 92-99. https://doi.org/10.31197/atnaa.692948
Goodman, A. (1991). On uniformly starlike functions. Journal of Mathematical Analysis and Applications, 155(2), 364-370.
Murugusundaramoorthy, G., Vijaya, K. and Porwal, S. (2016). Some inclusion results of certain subclass of analytic functions associated with Poisson distribution series. Hacettepe Journal of Mathematics and Statistics, 45(4), 1101-1107.
Porwal, S. (2014). An application of a Poisson distribution series on certain analytic functions. Journal of Complex Analysis, 2014, 1-3. http://dx.doi.org/10.1155/2014/984135
Porwal, S., Magesh, N. and Abirami, C. (2020). Certain subclasses of analytic functions associated with Mittag–Lefflertype Poisson distribution series. Boletín de la Sociedad Matemática Mexicana, 26(3), 1035-104. https://doi.org/10.1007/s40590-020-00288-x
Silverman, H. (1975). Univalent functions with negative coefficients. Proceedings of the American Mathematical Society, 51(1), 109-116.
Subramanian, K., Murugusundaramoorthy, G., Balasubrahmanyam, P. and Silverman, H. (1995). Subclasses of uniformly convex and uniformly starlike functions. Mathematica Japonicae, 42(3), 517–522.