• Nunokawa, Mamoru (University of Gunma) ;
  • Owa, Shigeyoshi (Kinki University) ;
  • Sokol, Janusz (Department of Mathematics Rzeszow University of Technology)
  • Received : 2015.01.27
  • Published : 2016.01.31


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


analytic;meromorphic;convex;starlike;univalent;Nunokawa's lemma;Briot-Bouquet;differential subordination


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