Abstract
Denote by $\cal A'$, the class of functions $f$, analytic in $E$ which satisfy $f(0)=1$. Let $\alpha >0, \beta \in (0,1]$ be real numbers and let $\gamma, {\rm Re} \gamma >0$, be a complex number. For $p, q \in \cal A'$, the authors study the differential subordination of the form $$(p(z))^\alpha \left[1+\frac {\gamma zp'(z)}{p(z)}\right]^\beta \prec(q(z))^\alpha \left[1+\frac {\gamma zq'(z)}{q(z)}\right]^\beta, z\in E,$$ and obtain its best dominant. Its applications to univalent functions are also given.
Citation
Sushma Gupta. Sukhjit Singh. "On Certain Differential Subordination and its Dominant." Bull. Belg. Math. Soc. Simon Stevin 12 (2) 259 - 274, June 2005. https://doi.org/10.36045/bbms/1117805088
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