On some starlike and convex functions
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- by G. M. Shah PDF
- Trans. Amer. Math. Soc. 154 (1971), 83-91 Request permission
Abstract:
In this paper we study functions of the form $\smallint _0^z(g(t)/\Pi _{k = 1}^n{(1 - t{z_k})^{{\alpha _k}}})$ for $|z| < 1$ and show under what conditions such a function is convex, convex in one direction and hence univalent in $|z| < 1$. We also study the functions $g(z)$ where $g(0) = 1,g(z) \ne 0$ and $\operatorname {Re} \;[zg’(z)/g(z)] \geqq - \alpha ,0 \leqq \alpha < 1$, for $|z| < 1$.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 154 (1971), 83-91
- MSC: Primary 30.42
- DOI: https://doi.org/10.1090/S0002-9947-1971-0269826-8
- MathSciNet review: 0269826