New Results Related to the Convexity and Starlikeness of the Bernardi Integral Operator

G. İ. OROS; Georgia İrina OROS

Makale detayları

New Results Related to the Convexity and Starlikeness of the Bernardi Integral Operator

Yazarlar:

G. İ. OROS | Georgia İrina OROS

Yayıncı:

Hacettepe University

Ana Başlıklar:

Analiz

Dergi:

Hacettepe Journal of Mathematics and Statistics 2009 Vol.38 Issue 2, pp.137-143

Belge Tipi:

Makale

Yayın Tarihi:

1/2009

Belge Dili:

İngilizce

Document ID (Org No.):

2000453748

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

Özet:

 

In (Lewandowski, Z., Miller, S. S. and Zlotkiewicz, E. Generating functions for some classes of univalent functions, Proc. Amer. Math. Soc. 56, 111–117, 1976) and (Pascu, N. N. Alpha-close-to-convex functions, Romanian–Finish Seminar on Complex Analysis, Springer Berlin, 331– 335, 1979) it has been proved that the integral operator defined by S. D. Bernardi (Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135, 429–446, 1969) and given by (1) Lγ(f)(z) = F(z) = γ + 1z γ Z z 0 f(t)t γ−1 dt, z ∈ U preserves certain classes of univalent functions, such as the class of starlike functions, the class of convex functions and the class of closeto-convex functions. In this paper we determine conditions that a function f ∈ A needs to satisfy in order that the function F given by (1) be convex. We alsoprove two duality theorems between the classes K−12γand S∗, andbetween K−12γand S∗−12γ, respectively.

Makale detayları

New Results Related to the Convexity and Starlikeness of the Bernardi Integral Operator

Yazarlar: G. İ. OROS | Georgia İrina OROS

Yayıncı: Hacettepe University

Ana Başlıklar: Analiz

Dergi: Hacettepe Journal of Mathematics and Statistics 2009 Vol.38 Issue 2, pp.137-143

Belge Tipi: Makale

Yayın Tarihi: 1/2009

Belge Dili: İngilizce

Document ID (Org No.): 2000453748

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

Sayı

Yazarlar:

G. İ. OROS | Georgia İrina OROS

Yayıncı:

Hacettepe University

Ana Başlıklar:

Analiz

Dergi:

Hacettepe Journal of Mathematics and Statistics 2009 Vol.38 Issue 2, pp.137-143

Belge Tipi:

Makale

Yayın Tarihi:

1/2009

Belge Dili:

İngilizce

Document ID (Org No.):

2000453748

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X