Sufficient Conditions for Janowski Starlikeness

Ali, Rosihan M.; Ravichandran, V.; Seenivasagan, N.

doi:https://doi.org/10.1155/2007/62925

International Journal of Mathematics and Mathematical Sciences

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Research Article | Open Access

Volume 2007 | Article ID 062925 | https://doi.org/10.1155/2007/62925

Sufficient Conditions for Janowski Starlikeness

Rosihan M. Ali,¹V. Ravichandran,¹and N. Seenivasagan¹

Academic Editor: Teodor Bulboaca

Received10 Mar 2007

Revised15 Jun 2007

Accepted04 Jul 2007

Published14 Aug 2007

Abstract

Let A,B,D,E∈[−1,1] and let p(z) be an analytic function defined on the open unit disk, p(0)=1. Conditions on A, B, D, and E are determined so that 1+βzp'(z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz). Similar results are obtained by considering the expressions 1+β(zp'(z)/p(z)) and 1+β(zp'(z)/p2(z)). These results are then applied to obtain sufficient conditions for analytic functions to be Janowski starlike.

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Copyright

Copyright © 2007 Rosihan M. Ali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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