A criterion for bounded functions
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We consider a sufficient condition for $w(z)$, analytic in $|z|<1$, to be bounded in $|z|<1$, where $w(0)=w'(0)=0$. We apply it to the meromorphic starlike functions. Also, a certain Briot-Bouquet differential subordination is considered. Moreover, we prove that if $p(z)+zp'(z)\phi(p(z))\prec h(z)$, then $p(z)\prec h(z)$, where $h(z)=[(1+z)(1-z)]^{\alpha}$, under some additional assumptions on $\phi(z)$.
Abstract
We consider a sufficient condition for $w(z)$, analytic in $|z|<1$, to be bounded in $|z|<1$, where $w(0)=w'(0)=0$. We apply it to the meromorphic starlike functions. Also, a certain Briot-Bouquet differential subordination is considered. Moreover, we prove that if $p(z)+zp'(z)\phi(p(z))\prec h(z)$, then $p(z)\prec h(z)$, where $h(z)=[(1+z)(1-z)]^{\alpha}$, under some additional assumptions on $\phi(z)$.
참고문헌 (10)
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