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

Year 2018, , 37 - 45, 30.11.2018

Hüseyin Baba

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.

Keywords

Univalent function, Fixed point, Starlike, Convex, Sălăgean operator

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

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.

Keywords

Ünivalent fonksiyon, Sabit nokta, Yıldızıl, Konveks, Sălăgean operatörü

References

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