New criteria for meromorphic convex functions

Authors : M. K. AOUF

Pages : 0-0

Doi:10.1501/Commua1_0000000321

View : 6 | Download : 6

Publication Date : 2005-01-01

Article Type : Research Paper

Abstract :Let Q insert ignore into journalissuearticles values(a); be the class of functions of the form f insert ignore into journalissuearticles values(z); = 1 + a.k z k insert ignore into journalissuearticles values(a -! 0); z *=o which are regular in the punctured disc U* = {z : 0 < |z| < 1} and satisfy- ing and n € No — {0,1,2,...}, where D n f insert ignore into journalissuearticles values(z); = + Y `fc n a fc_2 zfc- 2 . z fc=2 It is proved that Qn+ı insert ignore into journalissuearticles values(a); C Qn insert ignore into journalissuearticles values(a);. Since Qo insert ignore into journalissuearticles values(a); is the class of meromor- plıically convex functions of order ainsert ignore into journalissuearticles values(0 < a < 1); the members of Qn insert ignore into journalissuearticles values(a); are nıeromorfically convex . Further property preserviug integrals are considered.
Keywords : meromorphic, functions, convex