Some special differential subordinations

Yıl 2019, Cilt: 48 Sayı: 4, 1017 - 1034, 08.08.2019

Nisha Bohra Sushil Kumar V. Ravichandran

Öz

For an analytic function $p$ satisfying $p(0)=1$, we obtain sharp estimates on $\beta$ such that  the first order differential subordination $p(z)+\beta zp'(z)\prec \mathcal{P}(z)$ or  $1+\beta zp'(z)/p^{j}(z)\prec \mathcal{P}(z)$, $(j=0,1,2)$ implies $p(z)\prec \mathcal{Q}(z)$ where $\mathcal{P}$ and $\mathcal{Q}$ are Carathéodory functions. The key tools in the proof of main results are the theory of differential subordination  and some properties of hypergeometric functions. Further, these subordination results immediately give sufficient conditions for  an analytic function $f$ to be in various well-known subclasses of starlike functions.

Anahtar Kelimeler

differential subordination, starlike function, lemniscate of Bernoulli, sine, Janowski function, exponential function, rational function, hypergeometric function

Kaynakça

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