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Abstract
The objective of this paper is to obtain an upper bound of the third
order Hankel determinant for the inverse of the function f, when f belongs to
the reciprocal of bounded turning functions with new approach.
Mathematics Subject Classification (2010): 30C45, 30C50.
Results & Lemmas (4)
Each result is auto-extracted from the paper via OCR - the math is shown verbatim and may carry occasional transcription artifacts. Click to expand the full statement.
Lemma 1.2.
Lemma 1.2. ([10]) If g ∈P, then the sharp estimate |cn −µckcn−k| ≤2, holds for n, k ∈N = 1, 2, 3..., with n > k and µ ∈[0, 1].
Lemma 1.2. ([10]) If g ∈P, then the sharp estimate |cn −µckcn−k| ≤2, holds for n, k ∈N = {1, 2, 3...} , with n > k and µ ∈[0, 1].
Lemma 1.3.
Lemma 1.3. ([18]) If g ∈P, then the sharp estimate |cn −ckcn−k| ≤2, holds for n, k ∈N, with n > k.
Lemma 1.3. ([18]) If g ∈P, then the sharp estimate |cn −ckcn−k| ≤2, holds for n, k ∈N, with n > k.
Lemma 1.4.
Lemma 1.4. ([22]) If g ∈P then |ck| ≤2, for each k ≥1 and the inequality is sharp for the mobious transformation g(z) = 1+z 1−z, z ∈Ud. In…
Lemma 1.4. ([22]) If g ∈P then |ck| ≤2, for each k ≥1 and the inequality is sharp for the mobious transformation g(z) = 1+z 1−z, z ∈Ud. In order to obtain our result, we referred to the classical method devised by Libera and Zlotkiewicz [17], used by several authors. 2. Main result
Theorem 2.1.
Theorem 2.1. If f ∈ z | RT and f −1(w) = w + P n≥2 qnwn near the origin i.e., w = 0 is the inverse function of f, given in (1.1) then…
Theorem 2.1. If f ∈ z}|{ RT and f −1(w) = w + P n≥2 qnwn near the origin i.e., w = 0 is the inverse function of f, given in (1.1) then |H3,1(f −1)| ≤527 540.
Function classes studied:
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