On the algebraic properties of the univalent functions in class S

Year 2017, Volume: 5 Issue: 3, 293 - 298, 01.07.2017

İsmet Yildiz Hasan Sahin , Neslihan Uyanik

Abstract

This work is shown below, the algebraic sum of the two functions selected from class S of univalent functions which is a subclass of this class A of functions f(z) satisfy the conditions analiytic in the open unit disk U={z∈C:|z|<1} normalized with f(0)=0 and f'(0)=1 is not univalent.

Keywords

Algebraic sum, analitik functions

References

• Koichi Sakaguchi,On a Certain Univalent Mapping,Journal of Mathematical Society of Japan ,1959, Vol.11 No.1.
• M. Nunokawa , M. Aydo gan , K. Kuroki , I. Yildiz , S.Owa, n the order of close-to-convexity of convex functions of order alpha, Journal of Inequalities and Applications 2012, 2012:245 doi:10.1186/1029-242X- 2012-245.
• M. Nunokawa , M. Aydo gan , K. Kuroki , I. Yildiz , S.Owa, Some properties concerning close-to-convexity of certain analytic functions, Journal of Inequalities and Applications 2012, 2012:2.
• Nikola Tuneski, Some Results on Starlike and Convex Functions,Applicable analysis and Discrete Mathematics,2007,293-298.
• Peter L. Duren,Univalent Functions,Springer-Verlag New York,1983.
• Shigeyoshi Owa,The order of ,close-to-Convexity for Certain Univalent Functions,Journal of Mathematical Analysis and Applications1989,138,393-396.
• T. Hayami , H.Shiraishi , S.Owa, I. Yildiz , Notes on Nunokawa Lemmas,International Journal of Applied Mathematics 2012, 429-441.
• Vanessa Bertoni,Dimitri K. Dimitrov,Generating Starlike and Convex Univalent Functions,Mathematica Balkanica New Series Vol.19,2005,Fasc.3-4.