On a Problem of Univalence of Functions Satisfying a Differential Inequality

Sukhwinder Singh, Sushma Gupta and Sukhjit Singh

Sukhwinder Singh
Deaprtment of Applied Sciences
B.B.S.B. Engineering College
Fatehgarh Sahib-140 407 (Punjab) India
e-mail: ss_billing@yahoo.co.in

Sushma Gupta and Sukhjit Singh
Department of Mathematics
S.L.I.E.T., Longowal-148 106 (Punjab) India
e-mail: sushmagupta1@yahoo.com
sukhjit_d@yahoo.com

Abstract

In the present paper, the authors study the univalence of analytic functions expressed by certain differential inequality. This problem was initiated by Al-Amiri, H.S. and Reade M.O. in 1975. In 2005, it was investigated by Singh, V., Singh, S. and Gupta, S. We claim that our result contains the result of Singh, V., Singh, S. and Gupta, S. and improves the result of Al-Amiri, H.S. and Reade M.O. We also claim that our result is sharp in some sense.

http://www.mia-journal.com/cont.asp?what=miacont&vol=10