International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 8, Pages 563-568
Subordination by convex functions
Department of Mathematics, Punjabi University, Patiala 147002, (Punjab), India
Received 18 January 1990
Copyright © 2000 Ram Singh and Sukhjit Singh. 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.
Let , , denote the class of functions which are regular and univalently convex of order in the unit disc . Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if is regular in , and
in , then (i) at least in if ; and (ii) at least in if