Linear sums of certain analytic functions
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- by Ram Singh and Surinder Paul PDF
- Proc. Amer. Math. Soc. 99 (1987), 719-725 Request permission
Abstract:
Let $f$ belong to a certain subclass of the class of functions which are regular in the unit disc $E = \{ z:|z| < 1\}$. Suppose that $\phi = \phi (f,f’,f'')$ and $\psi = \psi (f,f’,f'')$ are regular in $E$ with $\operatorname {Re} \phi > 0$ in $E$ and $\operatorname {Re} \psi \ngtr 0$ in the whole of $E$. In this paper we consider the following two new types of problems: (i) To find the ranges of the real numbers $\lambda$ and $\mu$ such that $\operatorname {Re} (\lambda \phi + \mu \psi ) > 0$ in $E$. (ii) To determine the largest number $\rho ,0 < \rho < 1$, such that $\operatorname {Re} (\phi + \psi ) > 0$ in $|z| < \rho$.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 719-725
- MSC: Primary 30C45
- DOI: https://doi.org/10.1090/S0002-9939-1987-0877046-6
- MathSciNet review: 877046