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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Linear sums of certain analytic functions


Authors: Ram Singh and Surinder Paul
Journal: Proc. Amer. Math. Soc. 99 (1987), 719-725
MSC: Primary 30C45
MathSciNet review: 877046
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Abstract: Let $ f$ belong to a certain subclass of the class of functions which are regular in the unit disc $ E = \{ z:\vert z\vert < 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 $ \vert z\vert < \rho $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0877046-6
PII: S 0002-9939(1987)0877046-6
Article copyright: © Copyright 1987 American Mathematical Society