Some results on the Bazilevic functions B₁(α) related to the Lemniscate Bernouli (LB)

Abstract

This research is concerned with Bazilevic B1(α) on the unit disc D = {z| < 1}, related to the Lemniscate Bernoulli (LB), defined by kind of subordination for some positive alpha. There will be determined the Hankel determinant, especially the third Hankel determinant which B1(α) subordinates to LB, and we start with the case for starlike and convex functions, subset of B1(α). In this article we impeove the result of Kumar and Ravichandran.