On Some Results for a Subclass of Meromorphic Univalent Functions with Nonzero Pole

Bhowmik, Bappaditya; Parveen, Firdoshi

doi:10.1007/s00025-019-1118-4

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Sufficiency Is Obvious1

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2022

2023

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Cited by 3 publications

(2 citation statements)

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“…Corollary 2. (Compare [4]) Let f ∈ U m (λ) be as in the form of (5) with a simple pole at the point z = p, where the Laurent series of f at z = p is…”

Section: Sufficiency Is Obviousmentioning

confidence: 99%

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An elementary counterexample to a coefficient conjecture

Li¹,

Ponnusamy²,

Wirths³

2022

Preprint

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In this article, we consider the family of functions f meromorphic in the unit disk D = {z : |z| < 1} with a pole at the point z = p, a Taylor expansionand satisfying the conditionfor some λ, 0 < λ < 1. We denote this class by U m (λ) and we shall prove a representation theorem for the functions in this class. As consequences, we get a simple proof for the estimates of |a 2 | and obtain inequalities for the initial coefficients of the Laurent series of f ∈ U m (λ) at its pole. In [8] it had been conjectured that for f ∈ U m (λ) the inequalitiesare valid. We provide a counterexample to this conjecture for the case n = 3.

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“…Corollary 2. (Compare [4]) Let f ∈ U m (λ) be as in the form of (5) with a simple pole at the point z = p, where the Laurent series of f at z = p is…”

Section: Sufficiency Is Obviousmentioning

confidence: 99%

“…As the title indicates, the main aim of this paper is to disprove the conjecture (4). We want to emphasize at this place that some of the other results can be found in [2,3,4]. As a byproduct of main concern, we include some easy consequences of our discussion in the form of corollaries.…”

Section: Introductionmentioning

confidence: 98%