Sufficient Conditions for Starlike Functions Associated with the Lemniscate of Bernoulli

الأصل · EN

Let -1≤ B<A≤ 1. Condition on β, is determined so that 1+βzp'(z)/pᵏ(z)(1+Az)/(1+Bz)(-1<k≤3) implies p(z) √1+z. Similarly, condition on βis determined so that 1+βzp'(z)/pⁿ(z) or p(z)+βzp'(z)/pⁿ(z)√1+z(n=0, 1, 2) implies p(z)(1+Az)/(1+Bz) or √1+z. In addition to that condition on βis derived so that p(z)(1+Az)/(1+Bz) when p(z)+βzp'(z)/p(z)√1+z. Few more problems of the similar flavor are also considered.