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On Properties of the Subclass P(j,λ,α,n,𝑧0 ) of Starlike Functions

Year 2018, , 37 - 45, 30.11.2018
https://doi.org/10.17714/gumusfenbil.429431

Abstract

In this paper, we study the subclass P(j,λ,α,n,of starlike functions and with
negative coefficients by using the differential 
D^n operator and functions of the form f(z)=z-∑_(k=j+1)^∞ 〖a_k which are analytic in the open  unit disk. 
We consider the class 
P(j,λ,α,n,z_0) for which  z_0∈R ve f(z_0 )=z_0 real where  a_k≥0. Some  properties 
belonging  to  the 
class 
P(j,λ,α,n,z_0) are 
obtained.


References

  • Aouf, M.K. ve Srivastava, H.M., 1996. Some families of starlike functions with negative coefficients. Journal of Mathematical Analysis and Applications, 203, 762-790, Article No:0411.
  • Baba, H., 2018. The Modified Hadamard Products of Functions Belonging to the Class P(j,λ,α,n,z_0 ). International Journal of Scientific and Technological Research, 4 (3), 19-26.
  • Kiziltunc, H. ve Baba, H., 2012. Inequalities for Fixed Points of the Subclass P(j,λ,α,n) of Starlike Functions with Negative Coefficients. Advances in Fixed Point Theory, 2, 197-202.
  • Sălăgean, G.Şt., 1983. Subclasses of univalent functions. in "Complex Analysis: Fifth Romanian-Finnish Seminar." Part I (Bucharest, 1981), Lecture Notes in Mathematics, 1013, Springer-Verlag, Berlin/Newyork, pp. 362-372.
  • Silverman, H., 1975. Univalent functions with negative coefficients. Proceedings of the American Mathematical Society, 51, 109-116.
  • Silverman, H., 1976. Extreme points of univalent functions with two fixed points. Transactions of the American Mathematical Society, 219, 387-395.

Yıldızıl Fonksiyonların 𝑷(𝒋, 𝝀,𝜶, 𝒏, 𝒛𝟎) Alt Sınıfının Özellikleri

Year 2018, , 37 - 45, 30.11.2018
https://doi.org/10.17714/gumusfenbil.429431

Abstract

Bu makalede, açık birim diskte analitik olan 𝑓(𝑧) = 𝑧 − ∑ 𝑎𝑘𝑧 ∞ 𝑘 𝑘=𝑗+1 biçimindeki fonksiyonlar ve 𝐷 𝑛 diferansiyel operatörü kullanılarak negatif katsayılı yıldızıl fonksiyonların 𝑃(𝑗, 𝜆, 𝛼, 𝑛) alt sınıfına çalışıldı. 𝑎𝑘 ≥ 0 , 𝑧0 ∈ ℝ ve 𝑓(𝑧0) = 𝑧0 olan 𝑃(𝑗, 𝜆, 𝛼, 𝑛, 𝑧0) sınıfını göz önüne alındı. 𝑃(𝑗, 𝜆, 𝛼, 𝑛, 𝑧0) sınıfına ait bazı özellikler elde edildi.

References

  • Aouf, M.K. ve Srivastava, H.M., 1996. Some families of starlike functions with negative coefficients. Journal of Mathematical Analysis and Applications, 203, 762-790, Article No:0411.
  • Baba, H., 2018. The Modified Hadamard Products of Functions Belonging to the Class P(j,λ,α,n,z_0 ). International Journal of Scientific and Technological Research, 4 (3), 19-26.
  • Kiziltunc, H. ve Baba, H., 2012. Inequalities for Fixed Points of the Subclass P(j,λ,α,n) of Starlike Functions with Negative Coefficients. Advances in Fixed Point Theory, 2, 197-202.
  • Sălăgean, G.Şt., 1983. Subclasses of univalent functions. in "Complex Analysis: Fifth Romanian-Finnish Seminar." Part I (Bucharest, 1981), Lecture Notes in Mathematics, 1013, Springer-Verlag, Berlin/Newyork, pp. 362-372.
  • Silverman, H., 1975. Univalent functions with negative coefficients. Proceedings of the American Mathematical Society, 51, 109-116.
  • Silverman, H., 1976. Extreme points of univalent functions with two fixed points. Transactions of the American Mathematical Society, 219, 387-395.
There are 6 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Hüseyin Baba 0000-0001-9749-2299

Publication Date November 30, 2018
Submission Date June 1, 2018
Acceptance Date November 30, 2018
Published in Issue Year 2018

Cite

APA Baba, H. (2018). Yıldızıl Fonksiyonların 𝑷(𝒋, 𝝀,𝜶, 𝒏, 𝒛𝟎) Alt Sınıfının Özellikleri. Gümüşhane Üniversitesi Fen Bilimleri Dergisi37-45. https://doi.org/10.17714/gumusfenbil.429431