Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A CLASS OF MULTIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS DEFINED BY CONVOLUTION

  • Ali Rosihan M. (SCHOOL OF MATHEMATICAL SCIENCES, UNIVERSITI SAINS MALAYSIA) ;
  • Khan M. Hussain (DEPARTMENT OF MATHEMATICS, ISLAMIAH COLLEGE, VANIAMBADI) ;
  • Ravichandran V. (SCHOOL OF MATHEMATICAL SCIENCES, UNIVERSITI SAINS MALAYSIA) ;
  • Subramanian K.G. (DEPARTMENT OF MATHEMATICS, MADRAS CHRISTIAN COLLEGE, TAMBARAM)
  • Published : 2006.02.01
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Abstract

For a given p-valent analytic function g with positive coefficients in the open unit disk $\Delta$, we study a class of functions $f(z) = z^p - \sum\limits{_{n=m}}{^\infty} a_nz^n(a_n{\geq}0)$ satisfying $$\frac 1 {p}{\Re}\;(\frac {z(f*g)'(z)} {(f*g)(z)})\;>\;\alpha\;(0{\leq}\;\alpha\;<\;1;z{\in}{\Delta})$$ Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special cases.

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References

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