Sufficient conditions for starlike functions associated with the lemniscate of Bernoulli

By Sivaprasad Kumar, Virendra Kumar, V. Ravichandran, Nak Eun Cho. 2013

58 citations recorded by the source corpus.

Let −1≤B<A≤1. The 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, the condition on β is 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, the condition on β is derived so that p(z)≺(1+Az)/(1+Bz) when p(z)+βzp′(z)/p(z)≺1+z. A few more problems of the similar flavor are also considered.MSC:30C80, 30C45.

Subfields: Applied Mathematics, Geometry and Topology, Polymers and Plastics

View Paper: https://www.semanticscholar.org/paper/441ab1acae1a4fa4020a289211d42ea2dd56668a

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Starlikness Associated with Cosine Hyperbolic Function (2020, unknown): “[21,22], Paprocki and Sokół [23], Raza et al.”
The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛* (2019, background): “Some differential subordination results associated with lemniscate of Bernoulli is studied in [1,13].”