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Some results of the class functions with bounded radious rotation

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Author
Polatoğlu, Yaşar
Kahramaner, Yasemin
Yemişci, Halime Arzu
Type
Article
Date
2019
Language
en_US
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Abstract
Let A be the family of functions f(z) = z + a2z 2 + ... which are analytic in the open unit disc D = {z : |z| < 1}, and denote by P of functions p(z) = z + p1z + p2z 2 + ... analytic in D such that p(z) is in P if and only if p(z) ≺ 1 + z 1 − z ⇔ p(z) = 1 + φ(z) 1 − φ(z) , for some Schwarz function φ(z) and every z ∈ D. Let f(z) be an element of A, and satisfies the condition z f ′ (z) f(z) = k 4 + 1 2 p1(z) − k 4 − 1 2 p2(z) where p1(z), p2(z) ∈ P and k ≥ 2, then f(z) is called function with bounded radius rotation. The class of such functions is denoted by Rk. This class is generalization of starlike functions. The main purpose is to give some properties of the class Rk.
URI
https://hdl.handle.net/11413/4331
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İstanbul Kültür University

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Istanbul Kültür University, Ataköy Campus E5 Karayolu Üzeri Bakırköy 34158, İstanbul / TURKEY
Copyright © İstanbul Kültür University

Creative Commons Lisansı
IKU Institutional Repository, Creative Commons Alıntı-GayriTicari-Türetilemez 4.0 Uluslararası Lisansı ile lisanslanmıştır.

Designed by  UNIREPOS