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A CRITERION FOR BOUNDED FUNCTIONS

  • Nunokawa, Mamoru ;
  • Owa, Shigeyoshi ;
  • Sokol, Janusz
  • Received : 2015.01.27
  • Published : 2016.01.31

Abstract

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 ${\phi}(z)$.

Keywords

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

References

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Cited by

  1. NOTES ON THE PAPER "A CRITERION FOR BOUNDED FUNCTIONS" [BULL. KOREAN MATH. SOC. 53 (2016), NO. 1, 215-225] vol.53, pp.6, 2016, https://doi.org/10.4134/BKMS.b160197