International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 3, Pages 497-501
doi:10.1155/S0161171288000584

Some classes of alpha-quasi-convex functions

Khalida Inayat Noor

Mathematics Department, College of Science Education for Girls, Sitteen Road, Malaz, Riyadh, Saudi Arabia

Abstract

Let C[C,D], 1D<C1 denote the class of functions g, g(0)=0, g(0)=1, analytic in the unit disk E such that (zg(z))g(z) is subordinate to 1+CZ1+DZ, zE. We investigate some classes of Alpha-Quasi-Convex Functions f, with f(0)=f(0)1=0 for which there exists a gC[C,D] such that (1α)f(z)g(z)+α(zf(z))g(z) is subordinate to 1+AZ1+BZ, 1B<A1. Integral representation, coefficient bounds are obtained. It is shown that some of these classes are preserved under certain integral operators.