PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)Vol. 46(60), pp. 86--90 (1989)
|
|
PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 46(60), pp. 86--90 (1989) |
|
|
On $p$-valent analytic functions with reference to Bernardi and Ruscheweyh integral operatorsK. S. Padmanabhan and M. JayamalaThe Ramanujan Institute, University of Madras Madras 600005, India and Department of Mathematics, Queen Mary's College, Madras 600005, IndiaAbstract: Let $T_n(h)$ be the class of analytic functions in the unit disk $E$ of the form $f(z)=a_pz^p+\sum_{n=p+1}^{\infty} a_nz^n$, $p\ge 1$, which satisfy the condition, $\dfrac{(n+1)}{(n+p)}\dfrac{D^{n+1}f(z)}{D^nf(z)}\prec h(z)$, $z\in E$, where $h$ is a convex univalent function in $E$ with $h(0)=1$. Then it is proved that $f$ is preserved under the Bernardi integral operator under certain conditions. It is also shown that if $f\in T_0(h)$, it is preserved under the Ruscheweyh integral operator under certain conditions. Classification (MSC2000): 30C45 Full text of the article:
Electronic fulltext finalized on: 2 Nov 2001. This page was last modified: 16 Nov 2001.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
|