Results & Lemmas (4)
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Theorem 1.
Theorem 1. Recognize that class ϱt Σ(d, ϑ, l) is a member of the function f ∈Σ defined by reference (1). Then |k2| ≤ |td| p t |d| r 2 (1 +…
Theorem 1. Recognize that class ϱt Σ(d, ϑ, l) is a member of the function f ∈Σ defined by reference (1) . Then |k2| ≤ |td| p t |d| r 2 (1 + 2γ) ve−2v (td)2 −(1 + γ)2 e−2v (ϑtd2 + al)
Theorem 2.
Theorem 2. Recognize that class ϱt Σ(d, ϑ, l, γ) is a member of the function f ∈Σ defined by reference (1). Then k3 −ηk2 2 ≤ …
Theorem 2. Recognize that class ϱt Σ(d, ϑ, l, γ) is a member of the function f ∈Σ defined by reference (1) . Then k3 −ηk2 2 ≤ |td| 2(1+2γ)ve−2v ,
Corollary 1.
Corollary 1. Recognize that class ϱt Σ(d, ϑ, l) is a member of the function f ∈Σ defined by reference (1). Then
Corollary 1. Recognize that class ϱt Σ(d, ϑ, l) is a member of the function f ∈Σ defined by reference (1) . Then
Corollary 2.
Corollary 2. Recognize that class ϱt Σ(d, ϑ, l) is a member of the function f ∈Σ defined by reference (1). Then |k2| ≤ td √ td r 6ve−2v…
Corollary 2. Recognize that class ϱt Σ(d, ϑ, l) is a member of the function f ∈Σ defined by reference (1) . Then |k2| ≤ td √ td r 6ve−2v (td)2 −4e−2v (ϑtd2 + al)
Definitions (1)
Def 1.
Definition 1. In the event that the subordinations listed below are satisfied, a function denoted by (1) is considered to be a member of…
Definition 1. In the event that the subordinations listed below are satisfied, a function denoted by (1) is considered to be a member of the class ϱt Σ(d, ϑ, l, γ): (1 −γ)φPγf′(φ) Pγf(φ) + γ 1 + φPγf′′(φ) Pγf′(φ) ≺ψ(d, φ) + 1 −a
Function classes studied:
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