Convolution properties of a class of starlike functions
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- by Ram Singh and Sukhjit Singh PDF
- Proc. Amer. Math. Soc. 106 (1989), 145-152 Request permission
Abstract:
Let $R$ denote the class of functions $f(z) = z + {a_2}{z^2} + \cdots$ that are analytic in the unit disc $E = \{ z:\left | z \right | < 1\}$ and satisfy the condition $\operatorname {Re} (f’(z) + zf''(z)) > 0,z \in E$. It is known that $R$ is a subclass of ${S_t}$, the class of univalent starlike functions in $E$. In the present paper, among other things, we prove (i) for every $n \geq 1$, the $n$th partial sum of $f \in R,{s_n}(z,f)$, is univalent in $E$, (ii) $R$ is closed with respect to Hadamard convolution, and (iii) the Hadamard convolution of any two members of $R$ is a convex function in $E$.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 106 (1989), 145-152
- MSC: Primary 30C45
- DOI: https://doi.org/10.1090/S0002-9939-1989-0994388-6
- MathSciNet review: 994388