ON SUFFICIENT CONDITIONS FOR MULTIVALENT STARLIKENESS

  • Published : 2000.11.01

Abstract

Let's $S_n(p,\alpha)(p,n\in\ N={1,2,3,\cdots},0\leq\ \alpha<1)$ denote tje c;ass pf fimctopms $f(z)=z^p+a_{p+z}z^{p+n}+\cdots$ which are $\rho$-valently starlike of order $\alpha$ in the unit disk.Some criteria for a function f(z) to be in the class $S_n(\rho,\alpha)$ are given.

Keywords

References

  1. Rev. Roumaine Math. Pures Appl. v.29 On a Briot-Bouquet differential subordination P. Eenigenburg(et al)
  2. J. Math. Anal. Appl. v.65 Second order differential inequalities in the complex plane S. S. Miller;P. T. Mocamu
  3. Indian J. Pure Appl. Math. v.26 Notes on multivalent functions M. Nunokawa;S. Owa;H. Saitoh
  4. Internat. J. Math. and Math. Sci. v.17 A criterion for p-valently starlike functions S. Owa;M. Numokawa;S. Fukui
  5. Ann. Polon. Math. v.LXII Sufficient conditions for multivalent starlikeness S. Owa;M. Numokawa;H.Saitoh
  6. Bull. Austral. Math. Soc. v.41 An application of differential subordinations and some criteria for univalency S. Owa;M. Obradovic