A Version of Rouche's Theorem for Continuous Functions

Tsarpalias, A.

doi:10.2307/2324586

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“…Our version of Rouché's theorem is stronger than the versions given in [5, page 48] and [6]. At the end of the paper we give an application of our main result to a harmonic polynomial.…”

Section: Introductionmentioning

confidence: 82%

A Version of Rouché’s Theorem for Continuous Functions

Grigoryan¹

2014

Bull. Aust. Math. Soc.

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“…Our version of Rouché's theorem is stronger than the versions given in [5, page 48] and [6]. At the end of the paper we give an application of our main result to a harmonic polynomial.…”

Section: Introductionmentioning

confidence: 82%

A Version of Rouché’s Theorem for Continuous Functions

Grigoryan¹

2014

Bull. Aust. Math. Soc.

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Special Classes of Normal Families

Lappan

2007

Comput. Methods Funct. Theory

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The Symmetric Versions of Rouché’s Theorem via ∂--Calculus

Mortini

Rupp

2014

Journal of Complex Analysis

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Let (f,g) be a pair of holomorphic functions. In this expositional paper we apply the ∂--calculus to prove the symmetric version “|f+g|<|f|+|g| on ∂K” as well as the homotopic version of Rouché's theorem for arbitrary planar compacta K. Using Eilenberg's representation theorem we also give a converse to the homotopic version. Then we derive two analogs of Rouché's theorem for continuous-holomorphic pairs (a symmetric and a nonsymmetric one). One of the rarely presented properties of the non-symmetric version is that in the fundamental boundary hypothesis, |f+g|≤|g|, equality is allowed.

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A Version of Rouche's Theorem for Continuous Functions

Cited by 5 publications

References 1 publication

A Version of Rouché’s Theorem for Continuous Functions

A Version of Rouché’s Theorem for Continuous Functions

Special Classes of Normal Families

The Symmetric Versions of Rouché’s Theorem via ∂--Calculus

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