A note on neighborhoods of analytic functions having positive real part

Janice B. Walker

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-5

Abstract:

Let P denote the set of all functions analytic in the unit disk D = { z | | z | < 1 } having the form p ( z ) = 1 + ∑ k = 1 ∞ p k z k with Re { p ( z ) } > 0 . For δ ≥ 0 , let N δ ( p ) be those functions q ( z ) = 1 + ∑ k = 1 ∞ q k z k analytic in D with ∑ k = 1 ∞ | p k − q k | ≤ δ . We denote by P ′ the class of functions analytic in D having the form p ( z ) = 1 + ∑ k = 1 ∞ p k z k with Re { [ z p ( z ) ] ′ } > 0 . We show that P ′ is a subclass of P and detemine δ so that N δ ( p ) ⊂ P for p ∈ P ′ .

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:810670

DOI: 10.1155/S0161171290000643

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