Results & Lemmas (4)
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Lemma 3.1.
Lemma 3.1. (See [4]) Let ࣪ be the well-known class of Carathéodory functions, that is ܿ(ݖ) ∈ࣛ with the power series expansion
Lemma 3.1. (See [4]) Let ࣪ be the well-known class of Carathéodory functions, that is ܿ(ݖ) ∈ࣛ with the power series expansion
Lemma 3.2.
Lemma 3.2. (See [20]) If ܿ∈࣪, then
Lemma 3.2. (See [20]) If ܿ∈࣪, then
Lemma 3.3.
Lemma 3.3. (See [5]) The power series for ܿ converges in Δ to a function in ࣪ if and only if the Toeplitz determinants ܶ= ተ 2 ܿଵ ܿଶ ⋯ ܿ…
Lemma 3.3. (See [5]) The power series for ܿ converges in Δ to a function in ࣪ if and only if the Toeplitz determinants ܶ= ተ 2 ܿଵ ܿଶ ⋯ ܿ ܿିଵ 2 ܿଵ ⋯ ܿିଵ ⋮ ⋮
Theorem 3.4.
Theorem 3.4. Let ݂∈ℱΣ(ߣ, ߚ). Then |ܽଶܽସ−ܽଷ ଶ| ≤ ە ۖ ۖ ۖ ۖ ۔ ۖ ۖ ۖ ۖ ۓܪ(2),
Theorem 3.4. Let ݂∈ℱΣ(ߣ, ߚ). Then |ܽଶܽସ−ܽଷ ଶ| ≤ ە ۖ ۖ ۖ ۖ ۔ ۖ ۖ ۖ ۖ ۓܪ(2),
Definitions (1)
Def 2.1.
Definition 2.1. A function ݂∈Σ given by Eq. (1) is said to be in the class
Definition 2.1. A function ݂∈Σ given by Eq. (1) is said to be in the class
Function classes studied:
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